Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass

TL;DR

This paper investigates the quantum phase transition at zero temperature in a two-dimensional Ising spin-glass model using Monte Carlo simulations, estimating critical exponents and analyzing susceptibility behavior.

Contribution

It provides the first estimation of critical exponents for the 2D transverse field Ising spin-glass at zero temperature using finite-size scaling.

Findings

Critical exponents: z = 1.5 ± 0.05, ν = 1.0 ± 0.1

Both linear and non-linear susceptibilities diverge at the transition

Effective classical system in (2+1) dimensions studied via Monte Carlo

Abstract

We study the quantum transition at $T=0$ in the spin-$\frac12$ Ising spin--glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in (2+1) dimensions, which we study by Monte Carlo simulations. Values of the critical exponents are estimated by a finite-size scaling analysis. We find that the dynamical exponent, $z$, and the correlation length exponent, $\nu$, are given by $z = 1.5 \pm 0.05$ and $\nu = 1.0 \pm 0.1$. Both the linear and non-linear susceptibility are found to diverge at the critical point.