Field theory for zero temperature soft anharmonic spin glasses in a field

TL;DR

This paper develops a zero-temperature field theory for anharmonic soft spin glasses in a field, revealing critical behavior and finite-dimensional effects relevant to understanding spin glass transitions.

Contribution

It introduces a finite-dimensional anharmonic soft spin glass model and constructs a zero-temperature field theory with loop expansion, connecting to the KHGPS model and analyzing critical behavior.

Findings

Mean field limit matches the KHGPS model density of states.

Bare mass in the replicon sector remains positive at the transition.

Cubic couplings exhibit non-analytic behavior near the critical point.

Abstract

We introduce a finite dimensional anharmonic soft spin glass in a field and show how it allows the construction a field theory at zero temperature and the corresponding loop expansion. The mean field level of the model coincides with a recently introduced fully connected model, the KHGPS model, and it has a spin glass transition in a field at zero temperature driven by the appearance of pseudogapped non-linear excitations. We analyze the zero temperature limit of the theory and the behavior of the bare masses and couplings on approaching the mean field zero temperature critical point. Focusing on the so called replicon sector of the field theory, we show that the bare mass corresponding to fluctuations in this sector is strictly positive at the transition in a certain region of control parameter space. At the same time the two relevant cubic coupling constants $g_1$ and $g_2$ show a non-analytic behavior in their bare values: approaching the critical point at zero temperature, $g_1\to \infty$ while $g_2\propto T$ with a prefactor diverging at the transition. Along the same lines we also develop the field theory to study the density of states of the model in finite dimension. We show that in the mean field limit the density of states converges to the one of the KHGPS model. However the construction allows a treatment of finite dimensional effects in perturbation theory.