Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions

TL;DR

This study introduces a partial thermal boundary condition technique to analyze temperature and bond chaos in four-dimensional Gaussian spin glasses, revealing that bond chaos is significantly stronger and sharing similar scaling exponents with the $ ext{±J}$ model.

Contribution

The paper adapts thermal boundary conditions to partial boundary conditions in four dimensions, enabling efficient analysis of chaos in complex spin glass systems.

Findings

Bond chaos is much stronger than temperature chaos.

Both forms of chaos share the same scaling exponents.

Chaos influences the number of pure states in the system.

Abstract

Spin glasses have competing interactions and complex energy landscapes that are highly-susceptible to perturbations, such as the temperature or the bonds. The thermal boundary condition technique is an effective and visual approach for characterizing chaos, and has been successfully applied to three dimensions. In this paper, we tailor the technique to partial thermal boundary conditions, where thermal boundary condition is applied in a subset (3 out of 4 in this work) of the dimensions for better flexibility and efficiency for a broad range of disordered systems. We use this method to study both temperature chaos and bond chaos of the four-dimensional Edwards-Anderson model with Gaussian disorder to low temperatures. We compare the two forms of chaos, with chaos of three dimensions, and also the four-dimensional $\pm J$ model. We observe that the two forms of chaos are characterized by the same set of scaling exponents, bond chaos is much stronger than temperature chaos, and the exponents are also compatible with the $\pm J$ model. Finally, we discuss the effects of chaos on the number of pure states in the thermal boundary condition ensemble.