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arXiv · 1702.05474

A numerical study of the F-model with domain-wall boundaries

Rick Keesman·Jules Lamers
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Abstract

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multi-cluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyse local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Sylju{\aa}sen and Zvonarev, and recently studied by Lyberg et al. We point out '(anti)ferroelectric' oscillations close to the corresponding frozen regions as well as 'higher-order' oscillations forming an intricate pattern with saddle-point-like features.

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Rick Keesman, Jules Lamers. 2017-01-11. A numerical study of the F-model with domain-wall boundaries. https://doi.org/10.1103/physreve.95.052117

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