Fluctuation of the phase boundary in the six-vertex model with domain wall boundary conditions: a Monte Carlo study

Abstract

AbstractWe consider the six-vertex model with domain wall boundary conditions in a square lattice of dimensionN × N. Our main interest is the study of the fluctuations of the extremal lattice path about the arctic curves. We address the problem through Monte Carlo simulations. AtΔ=0, the fluctuations of the extremal path along any line parallel to the square diagonal were rigorously proven to follow the Tracy-Widom distribution. We provide strong numerical evidence that this is true also for other values of the anisotropy parameter Δ (0⩽Δ<1). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales asN1/3and provide a numerical estimate for the parameters of the scaling random variable.