Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model

TL;DR

This paper investigates the critical behavior of the transverse field Sherrington-Kirkpatrick spin glass model, revealing a crossover from classical to quantum universality classes at finite temperature through numerical simulations.

Contribution

It provides the first numerical evidence of a finite-temperature crossover in the critical behavior of a quantum spin glass model, supported by a tunneling-based theoretical argument.

Findings

Critical Binder cumulant and correlation length exponent cross over at finite temperature.

The crossover differs from pure systems where it occurs at zero temperature.

Numerical results support a tunneling-based qualitative explanation.

Abstract

We study the critical behavior of Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their `classical' to `quantum' values at a finite temperature (unlike the cases of pure systems where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.