# 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} }

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

### Delocalization of the height function of the six-vertex model

- 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…

### Correlation inequalities for the uniform 8-vertex model and the toric code model

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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…

### On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models

- MathematicsEntropy
- 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…

### Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model

- MathematicsCommunications 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.

### Rotational invariance in critical planar lattice models

- 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…

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