Critical interface: twisting spin glasses at $T_c$

TL;DR

This paper investigates the behavior of interface free-energy at the critical temperature in spin glasses, revealing that its leading scaling is independent of replica symmetry breaking and can be understood through simple cubic theory.

Contribution

It introduces a novel approach to analyze interface free-energy at $T_c$ in spin glasses using mean field theory and simple scaling arguments, independent of replica symmetry breaking.

Findings

Interface free-energy scales positively with system size at $T_c$

Scaling behavior is independent of replica symmetry breaking

Simple cubic theory suffices to describe critical interface behavior

Abstract

We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface free-energy that is positively defined and that should scale with a positive power of the system size in the spin glass phase. In this note we study the behavior of the interface at the spin glass critical temperature $T_c$ within mean field theory. We show that the leading scaling of the interface free-energy does not depend on replica symmetry breaking, and can be obtained by simple scaling arguments using a cubic theory for critical spin glasses.