An irreversible local Markov chain that preserves the six vertex model on a torus

TL;DR

This paper introduces an irreversible local Markov chain on six vertex model configurations on a torus, preserving Gibbs measures and exhibiting a conjectured nontrivial height function drift.

Contribution

It constructs a novel irreversible local Markov dynamics that preserves Gibbs measures for the six vertex model on a torus, with a conjectured height function drift.

Findings

Preserves Gibbs measures for the six vertex model

Features a conjecturally nontrivial height function drift

Provides a new Markov dynamics on lattice configurations

Abstract

We construct an irreversible local Markov dynamics on configurations of up-right paths on a discrete two-dimensional torus, that preserves the Gibbs measures for the six vertex model. An additional feature of the dynamics is a conjecturally nontrivial drift of the height function.