# On the Six-Vertex Model’s Free Energy

@article{DuminilCopin2020OnTS,
title={On the Six-Vertex Model’s Free Energy},
author={Hugo Duminil-Copin and Karol Kajetan Kozlowski and Dmitry Krachun and Ioan Manolescu and Tatiana Tikhonovskaia},
journal={Communications in Mathematical Physics},
year={2020},
volume={395},
pages={1383 - 1430}
}
• Published 21 December 2020
• Mathematics
• Communications in Mathematical Physics
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the regime Δ<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta <1… 6 Citations • Mathematics • 2020 We show that the height function of the six-vertex model, in the parameter range a = b = 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven • Physics • 2022 We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and • Mathematics Entropy • 2022 Several classical problems in symbolic dynamics concern the characterization of the simplex of measures of maximal entropy. For subshifts of finite type in higher dimensions, methods of statistical • Mathematics Communications in Mathematical Physics • 2022 In this paper we prove that the Euler–Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities. • Mathematics • 2020 In this paper, we prove that the large scale properties of a number of twodimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square ## References SHOWING 1-10 OF 53 REFERENCES • Mathematics • 2020 In this paper, we prove that the large scale properties of a number of twodimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square I prove that the Bethe roots describing either the ground state or a certain class of “particle-hole” excited states of the XXZ spin-1/2 chain in any sector with magnetisation$${\mathfrak{m} \in
• Mathematics
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We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1=2 chain in the disordered regime. In particular, we
At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits
• Mathematics
• 1966
The ground-state energy $2f$ per lattice site for an infinite system is studied as a function of $\ensuremath{\Delta}$ and of the magnetization $y$. Analyticity properties of \$f(\ensuremath{\Delta},
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