Critical behavior of the two-dimensional XY model
We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43...
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| Veröffentlicht in: | Physical review. B, Condensed matter Condensed matter, 1992-02, Vol.45 (6), p.2883-2898 |
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| container_title | Physical review. B, Condensed matter |
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| creator | RAJAN GUPTA BAILLIE, C. F |
| description | We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down. |
| doi_str_mv | 10.1103/PhysRevB.45.2883 |
| format | Article |
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F</creator><creatorcontrib>RAJAN GUPTA ; BAILLIE, C. F</creatorcontrib><description>We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down.</description><identifier>ISSN: 0163-1829</identifier><identifier>EISSN: 1095-3795</identifier><identifier>DOI: 10.1103/PhysRevB.45.2883</identifier><identifier>PMID: 10001838</identifier><identifier>CODEN: PRBMDO</identifier><language>eng</language><publisher>Woodbury, NY: American Physical Society</publisher><subject>665000 - Physics of Condensed Matter- (1992-) ; COMPUTERIZED SIMULATION ; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY ; Condensed matter: electronic structure, electrical, magnetic, and optical properties ; Exact sciences and technology ; General theory and models of magnetic ordering ; KOSTERLITZ-THOULESS THEORY ; MAGNETIC PROPERTIES ; Magnetic properties and materials ; MAGNETIC SUSCEPTIBILITY ; MATHEMATICAL MODELS ; MONTE CARLO METHOD ; PHYSICAL PROPERTIES ; Physics ; SCALING ; SIMULATION ; SPECIFIC HEAT ; Spin-glass and other random models ; STATISTICAL MODELS ; TEMPERATURE DEPENDENCE ; THERMODYNAMIC PROPERTIES</subject><ispartof>Physical review. 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F</creatorcontrib><title>Critical behavior of the two-dimensional XY model</title><title>Physical review. B, Condensed matter</title><addtitle>Phys Rev B Condens Matter</addtitle><description>We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down.</description><subject>665000 - Physics of Condensed Matter- (1992-)</subject><subject>COMPUTERIZED SIMULATION</subject><subject>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</subject><subject>Condensed matter: electronic structure, electrical, magnetic, and optical properties</subject><subject>Exact sciences and technology</subject><subject>General theory and models of magnetic ordering</subject><subject>KOSTERLITZ-THOULESS THEORY</subject><subject>MAGNETIC PROPERTIES</subject><subject>Magnetic properties and materials</subject><subject>MAGNETIC SUSCEPTIBILITY</subject><subject>MATHEMATICAL MODELS</subject><subject>MONTE CARLO METHOD</subject><subject>PHYSICAL PROPERTIES</subject><subject>Physics</subject><subject>SCALING</subject><subject>SIMULATION</subject><subject>SPECIFIC HEAT</subject><subject>Spin-glass and other random models</subject><subject>STATISTICAL MODELS</subject><subject>TEMPERATURE DEPENDENCE</subject><subject>THERMODYNAMIC PROPERTIES</subject><issn>0163-1829</issn><issn>1095-3795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNpNkM9LwzAUx4Mobk7vnqSIBy-deUnTJEcd_oKBIgp6CmmasEjbzKab7L-3o1N8l_d47_O-hw9Cp4CnAJhePS828cWub6YZmxIh6B4aA5YspVyyfTTGkNMUBJEjdBTjJ-6L5PIQjaCfQFAxRjBrfeeNrpLCLvTahzYJLukWNum-Q1r62jbRh6a_v38kdShtdYwOnK6iPdn1CXq7u32dPaTzp_vH2fU8NRRYl2YFA0YopzwrqNZa8Aw7TSxzHJekXwF3RkJecCyddIAz0BIzQazQUApJJ-h8yA2x8yoa31mzMKFprOkUJzzPJe2hywFatuFrZWOnah-NrSrd2LCKCgSTBHJGtygeUNOGGFvr1LL1tW43CrDa2lS_NlXG1NZm_3K2S18VtS3_PQz6euBiB-jYO3StboyPfxwDAiyn9AfPg3u9</recordid><startdate>19920201</startdate><enddate>19920201</enddate><creator>RAJAN GUPTA</creator><creator>BAILLIE, C. 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F</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c315t-4b515237374b3aaa8740fa2e5f70d2b3a17fc916b709f9f1041a90582e8a1d893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>665000 - Physics of Condensed Matter- (1992-)</topic><topic>COMPUTERIZED SIMULATION</topic><topic>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</topic><topic>Condensed matter: electronic structure, electrical, magnetic, and optical properties</topic><topic>Exact sciences and technology</topic><topic>General theory and models of magnetic ordering</topic><topic>KOSTERLITZ-THOULESS THEORY</topic><topic>MAGNETIC PROPERTIES</topic><topic>Magnetic properties and materials</topic><topic>MAGNETIC SUSCEPTIBILITY</topic><topic>MATHEMATICAL MODELS</topic><topic>MONTE CARLO METHOD</topic><topic>PHYSICAL PROPERTIES</topic><topic>Physics</topic><topic>SCALING</topic><topic>SIMULATION</topic><topic>SPECIFIC HEAT</topic><topic>Spin-glass and other random models</topic><topic>STATISTICAL MODELS</topic><topic>TEMPERATURE DEPENDENCE</topic><topic>THERMODYNAMIC PROPERTIES</topic><toplevel>online_resources</toplevel><creatorcontrib>RAJAN GUPTA</creatorcontrib><creatorcontrib>BAILLIE, C. F</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Physical review. B, Condensed matter</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>RAJAN GUPTA</au><au>BAILLIE, C. F</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Critical behavior of the two-dimensional XY model</atitle><jtitle>Physical review. B, Condensed matter</jtitle><addtitle>Phys Rev B Condens Matter</addtitle><date>1992-02-01</date><risdate>1992</risdate><volume>45</volume><issue>6</issue><spage>2883</spage><epage>2898</epage><pages>2883-2898</pages><issn>0163-1829</issn><eissn>1095-3795</eissn><coden>PRBMDO</coden><abstract>We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down.</abstract><cop>Woodbury, NY</cop><pub>American Physical Society</pub><pmid>10001838</pmid><doi>10.1103/PhysRevB.45.2883</doi><tpages>16</tpages></addata></record> |
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| source | American Physical Society Journals |
| subjects | 665000 - Physics of Condensed Matter- (1992-) COMPUTERIZED SIMULATION CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY Condensed matter: electronic structure, electrical, magnetic, and optical properties Exact sciences and technology General theory and models of magnetic ordering KOSTERLITZ-THOULESS THEORY MAGNETIC PROPERTIES Magnetic properties and materials MAGNETIC SUSCEPTIBILITY MATHEMATICAL MODELS MONTE CARLO METHOD PHYSICAL PROPERTIES Physics SCALING SIMULATION SPECIFIC HEAT Spin-glass and other random models STATISTICAL MODELS TEMPERATURE DEPENDENCE THERMODYNAMIC PROPERTIES |
| title | Critical behavior of the two-dimensional XY model |
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