No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model

TL;DR

This paper extends previous results to show that a scalar Ginzburg-Landau model with random fields and temperatures does not exhibit a spin glass phase, as the spin glass susceptibility cannot diverge independently.

Contribution

The authors generalize the absence of a spin glass phase from the Ising model to a scalar Ginzburg-Landau model with randomness in magnetic field and temperature.

Findings

Spin glass susceptibility cannot diverge without ferromagnetic susceptibility diverging.

No spin glass phase exists in the considered scalar Ginzburg-Landau model.

Generalization of previous Ising model results to a continuous spin model.

Abstract

Krzakala, Ricci-Tersenghi and Zdeborova have shown recently that the random field Ising model with non-negative interactions and arbitrary external magnetic field on an arbitrary lattice does not have a static spin glass phase. In this paper we generalize the proof to a soft scalar spin version of the Ising model: the Ginzburg-Landau model with random magnetic field and random temperature-parameter. We do so by proving that the spin glass susceptibility cannot diverge unless the ferromagnetic susceptibility does.