Temperature Chaos and Bond Chaos in the Edwards-Anderson Ising Spin Glass : Domain-Wall Free-Energy Measurements

TL;DR

This study investigates temperature and bond chaos in four-dimensional $ ext{EA}$ Ising spin glasses by measuring domain-wall free-energy, entropy, and correlation functions, confirming droplet theory predictions through finite-size scaling analysis.

Contribution

The paper provides the first comprehensive numerical confirmation of the droplet theory's scaling relations for chaos exponents in 4D EA spin glasses, including temperature and bond chaos effects.

Findings

Exponents satisfy the scaling relation $oxed{ ext{zeta} = d_s/2 - heta}$ within numerical accuracy.

Temperature and bond chaos effects are described by a universal scaling function.

Results support the droplet theory as an appropriate framework for chaos in EA spin glasses.

Abstract

Domain-wall free-energy $\delta F$, entropy $\delta S$, and the correlation function, $C_{\rm temp}$, of $\delta F$ are measured independently in the four-dimensional $\pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\theta$, the fractal dimension of domain walls $d_{\rm s}$ and the chaos exponent $\zeta$ are extracted from the finite-size scaling analysis of $\delta F$, $\delta S$ and $C_{\rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\zeta=d_{\rm s}/2-\theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.