Critical Region for Droplet Formation in the Two-Dimensional Ising Model

Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−...
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Gespeichert in:

Autor*in:	Biskup, Marek [verfasserIn] Chayes, Lincoln Kotecký, Roman

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2003

Schlagwörter:	Critical Temperature Dimensionless Parameter Critical Region Ising Model Inverse Temperature

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2003

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 242(2003), 1-2 vom: 07. Okt., Seite 137-183
Übergeordnetes Werk:	volume:242 ; year:2003 ; number:1-2 ; day:07 ; month:10 ; pages:137-183

Links:	Volltext

DOI / URN:	10.1007/s00220-003-0946-x

Katalog-ID:	SPR002330555

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520			\|a Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system.
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allfields	10.1007/s00220-003-0946-x doi (DE-627)SPR002330555 (SPR)s00220-003-0946-x-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Critical Region for Droplet Formation in the Two-Dimensional Ising Model 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213 Chayes, Lincoln aut Kotecký, Roman aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 242(2003), 1-2 vom: 07. Okt., Seite 137-183 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183 https://dx.doi.org/10.1007/s00220-003-0946-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 242 2003 1-2 07 10 137-183
spelling	10.1007/s00220-003-0946-x doi (DE-627)SPR002330555 (SPR)s00220-003-0946-x-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Critical Region for Droplet Formation in the Two-Dimensional Ising Model 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213 Chayes, Lincoln aut Kotecký, Roman aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 242(2003), 1-2 vom: 07. Okt., Seite 137-183 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183 https://dx.doi.org/10.1007/s00220-003-0946-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 242 2003 1-2 07 10 137-183
allfields_unstemmed	10.1007/s00220-003-0946-x doi (DE-627)SPR002330555 (SPR)s00220-003-0946-x-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Critical Region for Droplet Formation in the Two-Dimensional Ising Model 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213 Chayes, Lincoln aut Kotecký, Roman aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 242(2003), 1-2 vom: 07. Okt., Seite 137-183 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183 https://dx.doi.org/10.1007/s00220-003-0946-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 242 2003 1-2 07 10 137-183
allfieldsGer	10.1007/s00220-003-0946-x doi (DE-627)SPR002330555 (SPR)s00220-003-0946-x-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Critical Region for Droplet Formation in the Two-Dimensional Ising Model 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213 Chayes, Lincoln aut Kotecký, Roman aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 242(2003), 1-2 vom: 07. Okt., Seite 137-183 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183 https://dx.doi.org/10.1007/s00220-003-0946-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 242 2003 1-2 07 10 137-183
allfieldsSound	10.1007/s00220-003-0946-x doi (DE-627)SPR002330555 (SPR)s00220-003-0946-x-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Critical Region for Droplet Formation in the Two-Dimensional Ising Model 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213 Chayes, Lincoln aut Kotecký, Roman aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 242(2003), 1-2 vom: 07. Okt., Seite 137-183 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183 https://dx.doi.org/10.1007/s00220-003-0946-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 242 2003 1-2 07 10 137-183
language	English
source	Enthalten in Communications in mathematical physics 242(2003), 1-2 vom: 07. Okt., Seite 137-183 volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183
sourceStr	Enthalten in Communications in mathematical physics 242(2003), 1-2 vom: 07. Okt., Seite 137-183 volume:242 year:2003 number:1-2 day:07 month:10 pages:137-183
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Critical Temperature Dimensionless Parameter Critical Region Ising Model Inverse Temperature
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container_title	Communications in mathematical physics
authorswithroles_txt_mv	Biskup, Marek @@aut@@ Chayes, Lincoln @@aut@@ Kotecký, Roman @@aut@@
publishDateDaySort_date	2003-10-07T00:00:00Z
hierarchy_top_id	253721628
id	SPR002330555
language_de	englisch
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author	Biskup, Marek
spellingShingle	Biskup, Marek misc Critical Temperature misc Dimensionless Parameter misc Critical Region misc Ising Model misc Inverse Temperature Critical Region for Droplet Formation in the Two-Dimensional Ising Model
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topic_title	Critical Region for Droplet Formation in the Two-Dimensional Ising Model Critical Temperature (dpeaa)DE-He213 Dimensionless Parameter (dpeaa)DE-He213 Critical Region (dpeaa)DE-He213 Ising Model (dpeaa)DE-He213 Inverse Temperature (dpeaa)DE-He213
topic	misc Critical Temperature misc Dimensionless Parameter misc Critical Region misc Ising Model misc Inverse Temperature
topic_unstemmed	misc Critical Temperature misc Dimensionless Parameter misc Critical Region misc Ising Model misc Inverse Temperature
topic_browse	misc Critical Temperature misc Dimensionless Parameter misc Critical Region misc Ising Model misc Inverse Temperature
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title	Critical Region for Droplet Formation in the Two-Dimensional Ising Model
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title_full	Critical Region for Droplet Formation in the Two-Dimensional Ising Model
author_sort	Biskup, Marek
journal	Communications in mathematical physics
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author_browse	Biskup, Marek Chayes, Lincoln Kotecký, Roman
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author-letter	Biskup, Marek
doi_str_mv	10.1007/s00220-003-0946-x
title_sort	critical region for droplet formation in the two-dimensional ising model
title_auth	Critical Region for Droplet Formation in the Two-Dimensional Ising Model
abstract	Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. © Springer-Verlag Berlin Heidelberg 2003
abstractGer	Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. © Springer-Verlag Berlin Heidelberg 2003
abstract_unstemmed	Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, $ λ_{Δ} $ and Δ are related via a universal equation that apparently is independent of the details of the system. © Springer-Verlag Berlin Heidelberg 2003
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title_short	Critical Region for Droplet Formation in the Two-Dimensional Ising Model
url	https://dx.doi.org/10.1007/s00220-003-0946-x
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author2	Chayes, Lincoln Kotecký, Roman
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doi_str	10.1007/s00220-003-0946-x
up_date	2024-07-04T02:38:41.081Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR002330555</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327161630.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2003 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-003-0946-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR002330555</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00220-003-0946-x-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Biskup, Marek</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Critical Region for Droplet Formation in the Two-Dimensional Ising Model</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2003</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2003</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L2, inverse temperature β>$ β_{c} $ and overall magnetization conditioned to take the value m⋆L2−2m⋆vL, where $ β_{c} $−1 is the critical temperature, m⋆=m⋆(β) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when vL3/2L−2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value $ Δ_{c} $ and a function $ λ_{Δ} $ such that the following holds: For Δ<$ Δ_{c} $, there are no droplets beyond log L scale, while for Δ>$ Δ_{c} $, there is a single, Wulff-shaped droplet containing a fraction $ λ_{Δ} $≥$ λ_{c} $=2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. 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Critical Region for Droplet Formation in the Two-Dimensional Ising Model

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