Correlation Critical Exponents for the Six-Vertex Model

TL;DR

This paper derives the asymptotic behavior of arrow correlations in the six-vertex model at small anisotropy, revealing power law decay and anomalous exponents using a fermionic approach independent of the exact solution.

Contribution

It introduces a novel fermionic representation method to analyze correlation decay and exponents in the six-vertex model without relying on its exact solution.

Findings

Arrow correlations decay as a power law at large distances.

The correlation decay exhibits an anomalous critical exponent.

The method provides a new approach to studying integrable models.

Abstract

The six-vertex model on a square lattice is "exactly solvable" because an exact formula for the free energy can be obtained by Bethe Ansatz. However, exact formulas for the correlations of local bulk observables, such as the orientation of the arrow at a given edge, are in general not available. In this paper we consider the isotropic "zero-field" six-vertex model at small |\Delta|. We derive the large-distance asymptotic formula of the arrow-arrow correlation, which displays a power law decay and an anomalous exponent. Our method is based on an interacting fermions representation of the six-vertex model and does not use any information obtained from the exact solution.