Long-range spin glass in a field at zero temperature

TL;DR

This paper introduces a novel theoretical approach to compute critical exponents of the zero-temperature spin glass transition in a one-dimensional long-range model, serving as a proxy for higher-dimensional systems, and provides benchmarks for numerical simulations.

Contribution

It develops a new loop expansion within the Bethe M-layer formalism tailored for this specific spin glass transition analysis.

Findings

Estimated critical exponents for the transition

Benchmarks for numerical simulations in larger systems

Validation of the theoretical approach against known results

Abstract

We compute the critical exponents of the zero-temperature spin glass transition in a field on a one-dimensional long-range model, a proxy for higher-dimensional systems. Our approach is based on a novel loop expansion within the Bethe $M$-layer formalism, whose adaptation to this specific case is detailed here. The resulting estimates provide crucial benchmarks for numerical simulations that can access larger system sizes in one dimension, thus offering a key test of the theory of spin glasses in a field.