Logarithmic corrections to finite-size scaling in the four-state Potts model
The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large...
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| Veröffentlicht in: | J. Stat. Phys.; (United States) 1988-08, Vol.52 (3-4), p.679-710 |
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| container_title | J. Stat. Phys.; (United States) |
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| creator | HAMER, C. J BATCHELOR, M. T BARBER, M. N |
| description | The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large chain length L as x +d/ln L + o((ln L)/sup /minus/1/), where x is the anomalous dimension of the associated primary scaling operator. For the gaps associated with the energy and magnetic operators, the values of the amplitudes d are in agreement with predictions of conformal invariance. The implications of these analytical results for the extrapolation of finite lattice data are discussed. Accurate estimates of x and d are found to be extremely difficult even with data available from large lattices, L approx.500. |
| doi_str_mv | 10.1007/bf01019724 |
| format | Article |
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J ; BATCHELOR, M. T ; BARBER, M. N</creator><creatorcontrib>HAMER, C. J ; BATCHELOR, M. T ; BARBER, M. N ; Univ. of New South Wales, Kensington (Australia)</creatorcontrib><description>The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large chain length L as x +d/ln L + o((ln L)/sup /minus/1/), where x is the anomalous dimension of the associated primary scaling operator. For the gaps associated with the energy and magnetic operators, the values of the amplitudes d are in agreement with predictions of conformal invariance. The implications of these analytical results for the extrapolation of finite lattice data are discussed. Accurate estimates of x and d are found to be extremely difficult even with data available from large lattices, L approx.500.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/bf01019724</identifier><identifier>CODEN: JSTPBS</identifier><language>eng</language><publisher>Heidelberg: Springer</publisher><subject>645400 - High Energy Physics- Field Theory ; 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-) ; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics ; ANALYTICAL SOLUTION ; ANGULAR MOMENTUM ; ANOMALOUS DIMENSION ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY ; CONFORMAL INVARIANCE ; CORRECTIONS ; CRYSTAL LATTICES ; CRYSTAL MODELS ; CRYSTAL STRUCTURE ; EIGENSTATES ; EIGENVALUES ; ENERGY GAP ; ENERGY LEVELS ; Exact sciences and technology ; EXCITED STATES ; EXTRAPOLATION ; FIELD THEORIES ; GROUND STATES ; HAMILTONIANS ; HEISENBERG MODEL ; INVARIANCE PRINCIPLES ; Lattice theory and statistics (ising, potts, etc.) ; MATHEMATICAL MODELS ; MATHEMATICAL OPERATORS ; MECHANICS ; NUMERICAL SOLUTION ; PARTICLE PROPERTIES ; PERTURBATION THEORY ; Physics ; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS ; QUANTUM FIELD THEORY ; QUANTUM MECHANICS ; QUANTUM OPERATORS ; SCALE DIMENSION ; SCALING LAWS ; SPIN ; STATISTICAL MECHANICS ; Statistical physics, thermodynamics, and nonlinear dynamical systems</subject><ispartof>J. Stat. Phys.; (United States), 1988-08, Vol.52 (3-4), p.679-710</ispartof><rights>1989 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c266t-d9268a472f30db5feb596ed7d543140d7eb3ba851d1f56fab21beb4e28ea35313</citedby><cites>FETCH-LOGICAL-c266t-d9268a472f30db5feb596ed7d543140d7eb3ba851d1f56fab21beb4e28ea35313</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7351777$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/6010354$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>HAMER, C. J</creatorcontrib><creatorcontrib>BATCHELOR, M. T</creatorcontrib><creatorcontrib>BARBER, M. N</creatorcontrib><creatorcontrib>Univ. of New South Wales, Kensington (Australia)</creatorcontrib><title>Logarithmic corrections to finite-size scaling in the four-state Potts model</title><title>J. Stat. Phys.; (United States)</title><description>The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large chain length L as x +d/ln L + o((ln L)/sup /minus/1/), where x is the anomalous dimension of the associated primary scaling operator. For the gaps associated with the energy and magnetic operators, the values of the amplitudes d are in agreement with predictions of conformal invariance. The implications of these analytical results for the extrapolation of finite lattice data are discussed. Accurate estimates of x and d are found to be extremely difficult even with data available from large lattices, L approx.500.</description><subject>645400 - High Energy Physics- Field Theory</subject><subject>656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)</subject><subject>657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics</subject><subject>ANALYTICAL SOLUTION</subject><subject>ANGULAR MOMENTUM</subject><subject>ANOMALOUS DIMENSION</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</subject><subject>CONFORMAL INVARIANCE</subject><subject>CORRECTIONS</subject><subject>CRYSTAL LATTICES</subject><subject>CRYSTAL MODELS</subject><subject>CRYSTAL STRUCTURE</subject><subject>EIGENSTATES</subject><subject>EIGENVALUES</subject><subject>ENERGY GAP</subject><subject>ENERGY LEVELS</subject><subject>Exact sciences and technology</subject><subject>EXCITED STATES</subject><subject>EXTRAPOLATION</subject><subject>FIELD THEORIES</subject><subject>GROUND STATES</subject><subject>HAMILTONIANS</subject><subject>HEISENBERG MODEL</subject><subject>INVARIANCE PRINCIPLES</subject><subject>Lattice theory and statistics (ising, potts, etc.)</subject><subject>MATHEMATICAL MODELS</subject><subject>MATHEMATICAL OPERATORS</subject><subject>MECHANICS</subject><subject>NUMERICAL SOLUTION</subject><subject>PARTICLE PROPERTIES</subject><subject>PERTURBATION THEORY</subject><subject>Physics</subject><subject>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</subject><subject>QUANTUM FIELD THEORY</subject><subject>QUANTUM MECHANICS</subject><subject>QUANTUM OPERATORS</subject><subject>SCALE DIMENSION</subject><subject>SCALING LAWS</subject><subject>SPIN</subject><subject>STATISTICAL MECHANICS</subject><subject>Statistical physics, thermodynamics, and nonlinear dynamical systems</subject><issn>0022-4715</issn><issn>1572-9613</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1988</creationdate><recordtype>article</recordtype><recordid>eNo9kE1LAzEURYMoWKsbf0EQV0I0L5kkM0stVoUBXeh6yGcbaScliQv99Y5UXb3NeZd7D0LnQK-BUnVjAgUKnWLNAZqBUIx0EvghmlHKGGkUiGN0Uso7pbRrOzFDfZ9WOse63kaLbcrZ2xrTWHBNOMQxVk9K_PK4WL2J4wrHEde1xyF9ZFKqrh6_pFoL3ibnN6foKOhN8We_d47elvevi0fSPz88LW57YpmUlbiOyVY3igVOnRHBG9FJ75QTDYeGOuUNN7oV4CAIGbRhYLxpPGu95oIDn6OLfW4qNQ7FTi3t2qZxnMoPcjLAp6Q5utpDNqdSsg_DLsetzp8D0OFH1nC3_JM1wZd7eKd_loasRxvL_4fiApRS_BtlXGkT</recordid><startdate>198808</startdate><enddate>198808</enddate><creator>HAMER, C. J</creator><creator>BATCHELOR, M. T</creator><creator>BARBER, M. N</creator><general>Springer</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>198808</creationdate><title>Logarithmic corrections to finite-size scaling in the four-state Potts model</title><author>HAMER, C. J ; BATCHELOR, M. T ; BARBER, M. N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c266t-d9268a472f30db5feb596ed7d543140d7eb3ba851d1f56fab21beb4e28ea35313</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1988</creationdate><topic>645400 - High Energy Physics- Field Theory</topic><topic>656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)</topic><topic>657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics</topic><topic>ANALYTICAL SOLUTION</topic><topic>ANGULAR MOMENTUM</topic><topic>ANOMALOUS DIMENSION</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY</topic><topic>CONFORMAL INVARIANCE</topic><topic>CORRECTIONS</topic><topic>CRYSTAL LATTICES</topic><topic>CRYSTAL MODELS</topic><topic>CRYSTAL STRUCTURE</topic><topic>EIGENSTATES</topic><topic>EIGENVALUES</topic><topic>ENERGY GAP</topic><topic>ENERGY LEVELS</topic><topic>Exact sciences and technology</topic><topic>EXCITED STATES</topic><topic>EXTRAPOLATION</topic><topic>FIELD THEORIES</topic><topic>GROUND STATES</topic><topic>HAMILTONIANS</topic><topic>HEISENBERG MODEL</topic><topic>INVARIANCE PRINCIPLES</topic><topic>Lattice theory and statistics (ising, potts, etc.)</topic><topic>MATHEMATICAL MODELS</topic><topic>MATHEMATICAL OPERATORS</topic><topic>MECHANICS</topic><topic>NUMERICAL SOLUTION</topic><topic>PARTICLE PROPERTIES</topic><topic>PERTURBATION THEORY</topic><topic>Physics</topic><topic>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</topic><topic>QUANTUM FIELD THEORY</topic><topic>QUANTUM MECHANICS</topic><topic>QUANTUM OPERATORS</topic><topic>SCALE DIMENSION</topic><topic>SCALING LAWS</topic><topic>SPIN</topic><topic>STATISTICAL MECHANICS</topic><topic>Statistical physics, thermodynamics, and nonlinear dynamical systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>HAMER, C. J</creatorcontrib><creatorcontrib>BATCHELOR, M. T</creatorcontrib><creatorcontrib>BARBER, M. N</creatorcontrib><creatorcontrib>Univ. of New South Wales, Kensington (Australia)</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>J. Stat. Phys.; (United States)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>HAMER, C. J</au><au>BATCHELOR, M. T</au><au>BARBER, M. N</au><aucorp>Univ. of New South Wales, Kensington (Australia)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Logarithmic corrections to finite-size scaling in the four-state Potts model</atitle><jtitle>J. Stat. Phys.; (United States)</jtitle><date>1988-08</date><risdate>1988</risdate><volume>52</volume><issue>3-4</issue><spage>679</spage><epage>710</epage><pages>679-710</pages><issn>0022-4715</issn><eissn>1572-9613</eissn><coden>JSTPBS</coden><abstract>The leading corrections to finite-size scaling predictions for eigenvalues of the quantum Hamiltonian limit of the critical four-state Potts model are calculated analytically from the Bethe ansatz equations for equivalent eigenstates of a modified XXZ chain. Scaled gaps are found to behave for large chain length L as x +d/ln L + o((ln L)/sup /minus/1/), where x is the anomalous dimension of the associated primary scaling operator. For the gaps associated with the energy and magnetic operators, the values of the amplitudes d are in agreement with predictions of conformal invariance. The implications of these analytical results for the extrapolation of finite lattice data are discussed. Accurate estimates of x and d are found to be extremely difficult even with data available from large lattices, L approx.500.</abstract><cop>Heidelberg</cop><pub>Springer</pub><doi>10.1007/bf01019724</doi><tpages>32</tpages></addata></record> |
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| ispartof | J. Stat. Phys.; (United States), 1988-08, Vol.52 (3-4), p.679-710 |
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| recordid | cdi_crossref_primary_10_1007_BF01019724 |
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| subjects | 645400 - High Energy Physics- Field Theory 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-) 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics ANALYTICAL SOLUTION ANGULAR MOMENTUM ANOMALOUS DIMENSION CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY CONFORMAL INVARIANCE CORRECTIONS CRYSTAL LATTICES CRYSTAL MODELS CRYSTAL STRUCTURE EIGENSTATES EIGENVALUES ENERGY GAP ENERGY LEVELS Exact sciences and technology EXCITED STATES EXTRAPOLATION FIELD THEORIES GROUND STATES HAMILTONIANS HEISENBERG MODEL INVARIANCE PRINCIPLES Lattice theory and statistics (ising, potts, etc.) MATHEMATICAL MODELS MATHEMATICAL OPERATORS MECHANICS NUMERICAL SOLUTION PARTICLE PROPERTIES PERTURBATION THEORY Physics PHYSICS OF ELEMENTARY PARTICLES AND FIELDS QUANTUM FIELD THEORY QUANTUM MECHANICS QUANTUM OPERATORS SCALE DIMENSION SCALING LAWS SPIN STATISTICAL MECHANICS Statistical physics, thermodynamics, and nonlinear dynamical systems |
| title | Logarithmic corrections to finite-size scaling in the four-state Potts model |
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