TY - JOUR

T1 - The square-lattice F model revisited: a loop-cluster update scaling study

AU - Weigel, Martin

AU - Janke, Wolfhard

PY - 2005/7/27

Y1 - 2005/7/27

N2 - 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.

AB - 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.

U2 - 10.1088/0305-4470/38/32/002

DO - 10.1088/0305-4470/38/32/002

M3 - Article

VL - 38

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

M1 - 7067

ER -