Antiferromagnetic Potts models on the square lattice: A high-precision Monte Carlo study

Sabino José Ferreira, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length ξ ∼ 5000; the data are consistent with ξ(β) = Aeβp(1 + a1e + ⋯) as β → ∝, with p ≈.1. The staggered susceptibility behaves as χstagg ∼ ξ5/3. For q = 4 the model is disordered (ξ ≲ 2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.

    Original languageEnglish (US)
    Pages (from-to)461-530
    Number of pages70
    JournalJournal of Statistical Physics
    Volume96
    Issue number3-4
    DOIs
    StatePublished - Aug 1999

    Keywords

    • Algorithm
    • Antiferromagnet
    • Cluster algorithm
    • Finite-size scaling
    • Monte Carlo
    • Phase transition, zero-temperature critical point
    • Potts model
    • Square lattice
    • Swendsen Wang algorithm, Wang Swendsen-Kotecký

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Fingerprint Dive into the research topics of 'Antiferromagnetic Potts models on the square lattice: A high-precision Monte Carlo study'. Together they form a unique fingerprint.

    Cite this