Critical Behavior of the Two-Dimensional Random Quantum Ising Ferromagnet

TL;DR

This paper investigates the quantum phase transition in a two-dimensional random Ising model using Monte Carlo simulations, revealing critical behavior similar to one-dimensional cases, including an infinite dynamical exponent and stretched exponential decay of correlations.

Contribution

It provides the first numerical evidence of critical behavior in 2D random quantum Ising models, highlighting similarities to 1D analytical results.

Findings

Dynamical exponent is infinite at criticality.

Typical correlations decay with a stretched exponential.

Possible divergence of average and typical correlation lengths.

Abstract

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension: the dynamical exponent is infinite and, at the critical point, the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point, there may be different exponents for the divergence of the average and typical correlation lengths, again as in one-dimension, but the evidence for this is less strong.