Phase coexistence of gradient Gibbs states
Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Biskup, Marek [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© by the authors 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Probability theory and related fields - Berlin : Springer, 1992, 139(2007), 1-2 vom: 11. Jan., Seite 1-39 |
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| Übergeordnetes Werk: |
volume:139 ; year:2007 ; number:1-2 ; day:11 ; month:01 ; pages:1-39 |
| Links: |
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| DOI / URN: |
10.1007/s00440-006-0013-6 |
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| Katalog-ID: |
SPR006000452 |
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| 100 | 1 | |a Biskup, Marek |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Phase coexistence of gradient Gibbs states |
| 264 | 1 | |c 2007 | |
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| 520 | |a Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. | ||
| 650 | 4 | |a Partition Function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Thermodynamic Limit |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Gibbs Measure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Phase Coexistence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Loop Condition |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kotecký, Roman |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Probability theory and related fields |d Berlin : Springer, 1992 |g 139(2007), 1-2 vom: 11. Jan., Seite 1-39 |w (DE-627)254638791 |w (DE-600)1462994-X |x 1432-2064 |7 nnns |
| 773 | 1 | 8 | |g volume:139 |g year:2007 |g number:1-2 |g day:11 |g month:01 |g pages:1-39 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00440-006-0013-6 |z lizenzpflichtig |3 Volltext |
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10.1007/s00440-006-0013-6 doi (DE-627)SPR006000452 (SPR)s00440-006-0013-6-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Phase coexistence of gradient Gibbs states 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © by the authors 2007 Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 Kotecký, Roman aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 139(2007), 1-2 vom: 11. Jan., Seite 1-39 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 https://dx.doi.org/10.1007/s00440-006-0013-6 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 139 2007 1-2 11 01 1-39 |
| spelling |
10.1007/s00440-006-0013-6 doi (DE-627)SPR006000452 (SPR)s00440-006-0013-6-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Phase coexistence of gradient Gibbs states 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © by the authors 2007 Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 Kotecký, Roman aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 139(2007), 1-2 vom: 11. Jan., Seite 1-39 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 https://dx.doi.org/10.1007/s00440-006-0013-6 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 139 2007 1-2 11 01 1-39 |
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10.1007/s00440-006-0013-6 doi (DE-627)SPR006000452 (SPR)s00440-006-0013-6-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Phase coexistence of gradient Gibbs states 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © by the authors 2007 Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 Kotecký, Roman aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 139(2007), 1-2 vom: 11. Jan., Seite 1-39 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 https://dx.doi.org/10.1007/s00440-006-0013-6 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 139 2007 1-2 11 01 1-39 |
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10.1007/s00440-006-0013-6 doi (DE-627)SPR006000452 (SPR)s00440-006-0013-6-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Phase coexistence of gradient Gibbs states 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © by the authors 2007 Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 Kotecký, Roman aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 139(2007), 1-2 vom: 11. Jan., Seite 1-39 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 https://dx.doi.org/10.1007/s00440-006-0013-6 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 139 2007 1-2 11 01 1-39 |
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10.1007/s00440-006-0013-6 doi (DE-627)SPR006000452 (SPR)s00440-006-0013-6-e DE-627 ger DE-627 rakwb eng Biskup, Marek verfasserin aut Phase coexistence of gradient Gibbs states 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © by the authors 2007 Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 Kotecký, Roman aut Enthalten in Probability theory and related fields Berlin : Springer, 1992 139(2007), 1-2 vom: 11. Jan., Seite 1-39 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 https://dx.doi.org/10.1007/s00440-006-0013-6 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 139 2007 1-2 11 01 1-39 |
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Enthalten in Probability theory and related fields 139(2007), 1-2 vom: 11. Jan., Seite 1-39 volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 |
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Enthalten in Probability theory and related fields 139(2007), 1-2 vom: 11. Jan., Seite 1-39 volume:139 year:2007 number:1-2 day:11 month:01 pages:1-39 |
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Biskup, Marek @@aut@@ Kotecký, Roman @@aut@@ |
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Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. 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Biskup, Marek |
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Biskup, Marek misc Partition Function misc Thermodynamic Limit misc Gibbs Measure misc Phase Coexistence misc Loop Condition Phase coexistence of gradient Gibbs states |
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Phase coexistence of gradient Gibbs states Partition Function (dpeaa)DE-He213 Thermodynamic Limit (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Phase Coexistence (dpeaa)DE-He213 Loop Condition (dpeaa)DE-He213 |
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Phase coexistence of gradient Gibbs states |
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Phase coexistence of gradient Gibbs states |
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Biskup, Marek |
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10.1007/s00440-006-0013-6 |
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phase coexistence of gradient gibbs states |
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Phase coexistence of gradient Gibbs states |
| abstract |
Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. © by the authors 2007 |
| abstractGer |
Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. © by the authors 2007 |
| abstract_unstemmed |
Abstract We consider the (scalar) gradient fields $ η_{a} $ = ($ η_{b} $)—with b denoting the nearest-neighbor edges in %$\mathbb{Z}^{2}%$—that are distributed according to the Gibbs measure proportional to %$\hbox{e}^{-\beta H(\eta)}\nu(d \eta)%$. Here H = ∑bV($ η_{b} $) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by imposing the loop condition %$\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}%$ for each plaquette (b1,b2,b3,b4) in %$\mathbb{Z}^{2}%$. For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., E $ η_{b} $ = 0. © by the authors 2007 |
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| title_short |
Phase coexistence of gradient Gibbs states |
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https://dx.doi.org/10.1007/s00440-006-0013-6 |
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Kotecký, Roman |
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10.1007/s00440-006-0013-6 |
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2024-07-03T20:10:06.223Z |
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| score |
7.400943 |