Overcoming system-size limitations in spin glasses

TL;DR

This paper explores a one-dimensional Ising spin chain with power-law interactions to study spin glasses, enabling larger system sizes and universality class tuning, revealing insights into the spin glass state and energy distributions.

Contribution

It introduces a tunable one-dimensional model that overcomes size limitations and bridges different universality classes in spin-glass simulations.

Findings

Results suggest a replica symmetry breaking scenario in the spin glass state.

Ground-state energy distributions differ between mean-field and non-mean-field models.

The model allows studying large systems across various universality classes.

Abstract

In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional Hamiltonians in that a large range of system sizes can be studied. In addition, the universality class of the model can be changed by tuning the power law exponent, thus allowing us to scan from the mean-field to long-range and short-range universality classes. We illustrate the advantages of this model by studying the nature of the spin glass state where our results hint towards a replica symmetry breaking scenario. We also compute ground-state energy distributions and show that mean-field and non-mean-field models are intrinsically different.