Quantum Spherical Spin Glass.Supersymmetry and Annealing

TL;DR

This paper demonstrates that the quantum spherical spin glass model exhibits supersymmetry leading to an exact annealed average, with quantum effects influencing thermodynamic properties and phase behavior.

Contribution

It reveals supersymmetry in the quantum spherical spin glass and shows that the annealed average is exact, providing new thermodynamic and phase diagram results.

Findings

Supersymmetry invariance of the effective action.

Annealed average is exact in this model.

Finite entropy at zero temperature and vanishing specific heat.

Abstract

We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of the Becchi-Rouet-Stora-Tyutin(BRST) supersymmetry. The Ward identities associated to this invariance indicate that the spin glass order parameter must vanish, and as a result the annealed average is exact in this model. We present new results for for the free energy, entropy and specific heat. Due to quantum effects the entropy remains finite and the specific het vanishes at zero temperature. results for the phase diagram coincide with those obtained by different formalisms. At zero temperature we derive the scaling behaviour with frequency of the dynamical susceptibility.