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

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, $ν$, are given by $z = 1.5 \pm 0.05$ and $ν= 1.0 \pm 0.1$. Both the linear and non-linear susceptibility are found to diverge at the critical point.