The two-point correlation function in the six-vertex model

TL;DR

This paper investigates the behavior of two-point correlation functions in the six-vertex model with domain wall boundary conditions, combining numerical simulations and analytical results, especially at the free fermionic point and other phases.

Contribution

It provides a comprehensive numerical analysis of correlation functions across different phases of the six-vertex model, including analytical results at the free fermionic point.

Findings

Exact correlation functions at the free fermionic point match numerical results.

Logarithmic decay of correlations in the disordered phase.

Exponential decay of correlations in the antiferroelectric phase.

Abstract

We study numerically the two-point correlation functions of height functions in the six-vertex model with domain wall boundary conditions. The correlation functions and the height functions are computed by the Markov chain Monte-Carlo algorithm. Particular attention is paid to the free fermionic point ($\Delta=0$), for which the correlation functions are obtained analytically in the thermodynamic limit. A good agreement of the exact and numerical results for the free fermionic point allows us to extend calculations to the disordered ($|\Delta|<1$) phase and to monitor the logarithm-like behavior of correlation functions there. For the antiferroelectric ($\Delta<-1$) phase, the exponential decrease of correlation functions is observed.