Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-01-11
J.Phys. A38 (2005) 7067-7092
Physics
Condensed Matter
Statistical Mechanics
28 pages, 11 figures, 4 tables, revised version as published
Scientific paper
10.1088/0305-4470/38/32/002
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.
Janke Wolfhard
Weigel Martin
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