Static chaos and scaling behaviour in the spin-glass phase

TL;DR

This paper explores static chaos in spin glasses, proposing a scaling theory for the spin-glass phase under magnetic field perturbations, and compares mean-field and droplet approaches to understand chaos exponents and critical dimensions.

Contribution

It introduces a scaling framework for static chaos in spin glasses and analyzes the effects of magnetic fields using mean-field and droplet models, relating chaos exponents to fixed point exponents.

Findings

Mean-field chaos exponents are likely exact in finite dimensions.

Zero-temperature fixed point exponent θ is close to (d-3)/2.

d=3 is identified as the lower critical dimension.

Abstract

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.