1-loop contribution to the dynamical exponents in spin glasses

TL;DR

This paper calculates first-order corrections to dynamical exponents in spin glasses near the critical temperature using epsilon-expansion, revealing that both exponents decrease with lower spatial dimensions.

Contribution

It provides the first-order epsilon-expansion corrections to the dynamical exponents in spin glasses at criticality, extending mean field results.

Findings

Both exponents x and z decrease as spatial dimension decreases.

First-order epsilon-expansion corrections are derived for the exponents.

Results suggest dimensional dependence of dynamical critical behavior.

Abstract

We evaluate the corrections to the mean field values of the $x$ and the $z$ exponents at the first order in the $\epsilon$-expansion, for $T=T_c $. We find that both $x$ and $z$ are decreasing when the space dimension decreases.