Percolation in two-dimensional lattices. II. The extent of universality
By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the...
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Gespeichert in:
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1989 |
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Online-Ressource 11 |
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APS Digital Backfile Archive 1893-2003 |
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Enthalten in: Physical review / B - College Park, Md. : APS, 1970, 40(1989), 1, Seite 650-660 |
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volume:40 ; year:1989 ; number:1 ; pages:650-660 ; extent:11 |
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| 520 | |a By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. | ||
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(DE-627)NLEJ249336723 (DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9 DE-627 ger DE-627 rakwb Percolation in two-dimensional lattices. II. The extent of universality 1989 Online-Ressource 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. APS Digital Backfile Archive 1893-2003 Yonezawa, Fumiko oth Sakamoto, Shoichi oth Enthalten in Physical review / B College Park, Md. : APS, 1970 40(1989), 1, Seite 650-660 Online-Ressource (DE-627)NLEJ248237845 (DE-600)1473011-X 1550-235X nnns volume:40 year:1989 number:1 pages:650-660 extent:11 https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 40 1989 1 650-660 11 |
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(DE-627)NLEJ249336723 (DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9 DE-627 ger DE-627 rakwb Percolation in two-dimensional lattices. II. The extent of universality 1989 Online-Ressource 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. APS Digital Backfile Archive 1893-2003 Yonezawa, Fumiko oth Sakamoto, Shoichi oth Enthalten in Physical review / B College Park, Md. : APS, 1970 40(1989), 1, Seite 650-660 Online-Ressource (DE-627)NLEJ248237845 (DE-600)1473011-X 1550-235X nnns volume:40 year:1989 number:1 pages:650-660 extent:11 https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 40 1989 1 650-660 11 |
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(DE-627)NLEJ249336723 (DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9 DE-627 ger DE-627 rakwb Percolation in two-dimensional lattices. II. The extent of universality 1989 Online-Ressource 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. APS Digital Backfile Archive 1893-2003 Yonezawa, Fumiko oth Sakamoto, Shoichi oth Enthalten in Physical review / B College Park, Md. : APS, 1970 40(1989), 1, Seite 650-660 Online-Ressource (DE-627)NLEJ248237845 (DE-600)1473011-X 1550-235X nnns volume:40 year:1989 number:1 pages:650-660 extent:11 https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 40 1989 1 650-660 11 |
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(DE-627)NLEJ249336723 (DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9 DE-627 ger DE-627 rakwb Percolation in two-dimensional lattices. II. The extent of universality 1989 Online-Ressource 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. APS Digital Backfile Archive 1893-2003 Yonezawa, Fumiko oth Sakamoto, Shoichi oth Enthalten in Physical review / B College Park, Md. : APS, 1970 40(1989), 1, Seite 650-660 Online-Ressource (DE-627)NLEJ248237845 (DE-600)1473011-X 1550-235X nnns volume:40 year:1989 number:1 pages:650-660 extent:11 https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 40 1989 1 650-660 11 |
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(DE-627)NLEJ249336723 (DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9 DE-627 ger DE-627 rakwb Percolation in two-dimensional lattices. II. The extent of universality 1989 Online-Ressource 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. APS Digital Backfile Archive 1893-2003 Yonezawa, Fumiko oth Sakamoto, Shoichi oth Enthalten in Physical review / B College Park, Md. : APS, 1970 40(1989), 1, Seite 650-660 Online-Ressource (DE-627)NLEJ248237845 (DE-600)1473011-X 1550-235X nnns volume:40 year:1989 number:1 pages:650-660 extent:11 https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 40 1989 1 650-660 11 |
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percolation in two-dimensional lattices. ii. the extent of universality |
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Percolation in two-dimensional lattices. II. The extent of universality |
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By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. |
| abstractGer |
By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. |
| abstract_unstemmed |
By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ249336723</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231114101601.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231114s1989 xx |||||o 00| ||und c</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ249336723</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-601)aps:424816860ee6c543188d59b0f80064b4b8c58bd9</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="245" ind1="1" ind2="0"><subfield code="a">Percolation in two-dimensional lattices. II. The extent of universality</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">11</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="520" ind1=" " ind2=" "><subfield code="a">By making use of finite-size scaling and Monte Carlo simulations, we study the so-called ‘‘universality’’ concerning critical exponents of percolation in several two-dimensional lattices. In particular, our main purpose is to clarify how universal is ‘‘universality.’’ For this purpose, we choose the following five lattices–square and kagome$iaa— (both periodic where the number z of nearest-neighbor sites is single valued, i.e., z=4), dice (periodic where z is mixed valued, i.e., z=3 and 6, the average z¯ being four), Penrose tiling (nonperiodic where z is mixed valued, i.e., z=3, 4, 5, 6, and 7, the average z¯ being four), and the dual lattice of Penrose (nonperiodic where z is single valued, i.e., z=4). For both site and bond percolation of these lattices, we analyze the results of our Monte Carlo simulations and evaluate six critical exponents, all of which are in good agreement with respective values predicted theoretically. Our results indicate that ‘‘universality’’ is really universal irrespective of classes of problems, i.e., whether bond or site; irrespective of kinds of lattices, i.e., whether periodic or nonperiodic; and irrespective of types of coordination, i.e., whether single valued or mixed valued.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">APS Digital Backfile Archive 1893-2003</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yonezawa, Fumiko</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sakamoto, Shoichi</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Physical review / B</subfield><subfield code="d">College Park, Md. : APS, 1970</subfield><subfield code="g">40(1989), 1, Seite 650-660</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ248237845</subfield><subfield code="w">(DE-600)1473011-X</subfield><subfield code="x">1550-235X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:40</subfield><subfield code="g">year:1989</subfield><subfield code="g">number:1</subfield><subfield code="g">pages:650-660</subfield><subfield code="g">extent:11</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/aps%3A424816860ee6c543188d59b0f80064b4b8c58bd9</subfield><subfield code="x">Verlag</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-APS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">40</subfield><subfield code="j">1989</subfield><subfield code="e">1</subfield><subfield code="h">650-660</subfield><subfield code="g">11</subfield></datafield></record></collection>
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