Replica symmetry breaking in the transverse-field Ising spin-glass model: Two frmionic representations

TL;DR

This paper investigates the quantum spin-glass phase of the infinite-range transverse-field Ising model using one-step replica symmetry breaking, comparing fermionic representations and analyzing phase transitions and stability.

Contribution

It introduces a comparison of two fermionic models for the transverse-field Ising spin-glass and applies one-step RSB to analyze phase transitions and stability.

Findings

Critical temperature decreases with increasing transverse field.

Both models exhibit a quantum critical point at the same field value.

The spin-glass phase is unstable under replica symmetry breaking.

Abstract

We analyze the infinite range Ising spin-glass in a transverse-field below the critical temperature by a one step replica symmetry theory(1S-RSB). The set of n replicas is divided in r blocks of m replicas each. We present results for different values of the block-size parameter m. The spin operators are represented by bilinear combinations of fermionic fields and we compare the results of two models: in the four state (4S)-model the diagonal S^z operator has two unphysical vanishing eigenvalues, that are suppressed by a restraint in the two states (2S)-model. In the static approximation we obtain qualitatively similar results for both models. They both exhibit a critical temperature that decreases when the transverse field increases,until it reaches a quantum critical point (QCP) at the same value of the critical field, and they are both unstable under replica symmetry breaking in the whole spin glass phase. Below the critical temperature we present results for the order parameters and free energy.