Vector breaking of replica symmetry in some low temperature disordered systems

TL;DR

This paper introduces a novel method for analyzing low-temperature disordered systems using the replicated Hamiltonian, emphasizing the importance of vector replica symmetry breaking saddle points for accurate scaling behavior.

Contribution

It presents a new approach that incorporates vector replica symmetry breaking saddle points, extending beyond traditional matrix sector analysis in disordered systems.

Findings

Vector replica symmetry breaking saddle points are crucial for certain disordered systems.

The method allows resummation of saddle point contributions to determine low-temperature scaling.

The approach broadens understanding of replica symmetry breaking beyond spin glass models.

Abstract

We present a new method to study disordered systems in the low temperature limit. The method uses the replicated Hamiltonian. It studies the saddle points of this Hamiltonian and shows how the various saddle point contributions can be resummed in order to obtain the scaling behaviour at low temperatures. In a large class of strongly disordered systems, it is necessary to include saddle points of the Hamiltonian which break the replica symmetry in a vector sector, as opposed to the usual matrix sector breaking of spin glass mean field theory.