The square-lattice F model revisited: a loop-cluster update scaling study

Abstract

The six-vertex F model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite-order phase transition of the Kosterlitz-Thouless type. As one of the few non-trivial exactly solved models, it provides a welcome gauge for new numerical simulation methods and scaling techniques. In view of the notorious problems of clearly resolving the Kosterlitz-Thouless scenario in the two-dimensional XY model numerically, the F model in particular constitutes an instructive reference case for the simulational description of this type of phase transition. We present a loop-cluster update Monte Carlo study of the square-lattice F model, with a focus on the properties not exactly known such as the polarizability or the scaling dimensions in the critical phase. For the analysis of the simulation data, finite-size scaling is explicitly derived from the exact solution and plausible assumptions. Guided by the available exact results, the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour.

28 pages, 11 figures, 4 tables, revised version as published

References in corpus (7)

• Power-law spin correlations in pyrochlore antiferromagnets
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Extracting short-distance physics from K_{L,S} -> pi0 e+ e- decays
• Directed-loop Monte Carlo simulations of vertex models
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Bulk and surface properties in the critical phase of the two-dimensional XY model
• The F model on dynamical quadrangulations

Cited by in corpus (9)

• Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior
• Classical topological order of the Rys F-model and its breakdown in realistic spin ice: Topological sectors of Faraday loops
• A numerical study of the F-model with domain-wall boundaries
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Domain wall fluctuations of the six-vertex model at the ice point
• The F model on dynamical quadrangulations
• Experimental Measures of Topological Sector Fluctuations in the F-Model
• Finite-size scaling at infinite-order phase transitions
• Phase transitions and crtical exponents in the six-vertex model on kagome lattices