The six-vertex model on random lattices

TL;DR

This paper analyzes the six-vertex model on random lattices, providing an exact solution at criticality and exploring its conformal field theory properties coupled to gravity.

Contribution

It introduces a matrix model formulation of the six-vertex model on dynamical lattices and derives its critical behavior and conformal properties.

Findings

Exact solution at criticality in the large N limit

Critical exponents vary continuously along the critical line

Model corresponds to a line of c=1 conformal field theories coupled to gravity

Abstract

In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large N planar limit, an exact solution is found at criticality. The critical exponents of the model are determined; they vary continously along the critical line. The vicinity of the latter is explored, which confirms that we have a line of c=1 conformal field theories coupled to gravity.