Infinite number of exponents for a spin glass transition

TL;DR

This paper demonstrates that an infinite set of critical exponents is necessary to describe the overlap behavior at the spin glass transition in directed polymers, using an epsilon expansion without replica methods.

Contribution

It introduces a novel epsilon expansion approach to analyze overlaps at the spin glass transition, avoiding the replica trick.

Findings

An infinite number of exponents are needed to characterize overlaps.

The analysis is performed in an epsilon expansion framework.

The method bypasses the traditional replica trick.

Abstract

We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a directed polymer in a random medium. We show that an infinite number of exponents is required to describe these overlaps. This is done in an $\epsilon = d-2$ expansion without using the replica trick.