Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass

TL;DR

This paper investigates how free energy fluctuations in large-$m$ component vector spin glasses scale with system size, revealing a connection to bond chaos and establishing a specific scaling exponent.

Contribution

It introduces a novel approach linking free energy fluctuations to bond chaos in the large-$m$ spin glass model, providing precise scaling exponents.

Findings

Free energy fluctuations scale as $N^er$ with $1/5 er < 3/10$.

The scaling exponent $er$ is very likely exactly $1/5$.

Bond chaos is quantitatively connected to free energy fluctuations.

Abstract

We calculate the finite size scaling of the sample-to-sample fluctuations of the free energy $\Delta F$ of the $m$ component vector spin glass in the large-$m$ limit. This is accomplished using a variant of the interpolating Hamiltonian technique which is used to establish a connection between the free energy fluctuations and bond chaos. The calculation of bond chaos then shows that the scaling of the free energy fluctuaions with system size $N$ is $\Delta F \sim N^\mu$ with ${1/5}\leq\mu <{3/10}$, and very likely $\mu={1}{5}$ exactly.