Direction dependent free energy singularity of the asymmetric six-vertex model

TL;DR

This paper investigates the phase transition behavior of the asymmetric six-vertex model, revealing a direction-dependent free energy singularity with a 3/2 exponent in most directions and a discontinuity in the third derivative along the tangential direction.

Contribution

It demonstrates the direction-dependent nature of free energy singularities in the asymmetric six-vertex model near the phase boundary.

Findings

Free energy exhibits a 3/2 power-law singularity in most directions.

Along the tangential direction, the free energy's third derivative is discontinuous.

The phase transition is characterized by Pokrovski-Talapov type behavior.

Abstract

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields $(h,v)$. In the $(h,v)$ plane, the phase boundary is approached along straight lines $\delta v=k \delta h$, where $(\delta h,\delta v)$ measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition $\delta f \sim const (\delta h)^{3/2}$ for any direction other than the tangential one. In the latter case $\delta f$ shows a discontinuity in the third derivative.