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

Martin Weigel, Wolfhard Janke

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6 Citations (Scopus)
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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 dimension 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.
Original languageEnglish
Article number7067
JournalJournal of Physics A: Mathematical and General
Volume38
DOIs
Publication statusPublished - 27 Jul 2005

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Square Lattice
Update
Scaling
scaling
Phase Transition
Phase transitions
XY Model
Model
data simulation
Finite-size Scaling
Monte Carlo Study
Exact Results
two dimensional models
Simulation Methods
Gauge
apexes
Inclusion
Exact Solution
Gages
Asymptotic Behavior

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The square-lattice F model revisited: a loop-cluster update scaling study. / Weigel, Martin; Janke, Wolfhard.

In: Journal of Physics A: Mathematical and General, Vol. 38, 7067, 27.07.2005.

Research output: Contribution to journalArticle

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