Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

TL;DR

This study uses Monte Carlo simulations to analyze the quantum phase transition in a two-dimensional random Ising model, revealing critical behavior and Griffiths-McCoy singularities similar to one-dimensional cases, with diverging susceptibility near the transition.

Contribution

It provides the first numerical evidence of critical behavior and Griffiths-McCoy singularities in the 2D random quantum Ising model, extending known 1D analytical results.

Findings

Infinite dynamical exponent at criticality

Stretched exponential decay of correlations

Diverging susceptibility in a parameter range

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. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.