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

Abstract

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