Frustration in vicinity of transition point of Ising spin glasses

TL;DR

This paper proposes a conjectured relationship between frustration and the critical transition point in various Ising spin glass models, linking frustration measures to phase transition thresholds.

Contribution

It introduces a novel conjecture connecting frustration derivatives to the zero-temperature transition point across multiple Ising spin glass models.

Findings

The conjecture holds for binary couplings on 2D and hierarchical lattices.

The relation aligns with the replica-symmetric solution in the SK model.

Provides a unified perspective on frustration and phase transitions.

Abstract

We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lattices, hierarchical lattices, and three-body Ising spin glasses with binary couplings on two-dimensional lattices. In addition, the same argument in the Sherrington-Kirkpatrick model yields a point that is identical to the replica-symmetric solution of the transition point at zero temperature.