Universality-class dependence of energy distributions in spin glasses

TL;DR

This study investigates how the probability distribution of ground-state energies in spin glasses varies across different universality classes, revealing non-Gaussian distributions in mean-field models and Gaussian in non-mean-field models, with implications for understanding disordered systems.

Contribution

It demonstrates the dependence of energy distribution shapes on universality class in spin glasses and compares one-dimensional and two-leg ladder models, providing new insights into their scaling behaviors.

Findings

Mean-field models have non-Gaussian energy distributions.

Non-mean-field models exhibit Gaussian energy distributions.

Skewness converges to a nonzero constant in mean-field universality class.

Abstract

We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price algorithms. By tuning the exponent of the power-law interactions we are able to scan several universality classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution. We compare the results of the disordered one-dimensional Ising chain to results for a disordered two-leg ladder, for which large system sizes can be studied, and find a qualitative agreement between the disordered one-dimensional Ising chain in the short-range universality class and the disordered two-leg ladder. We show that the mean and the standard deviation of the ground-state energy distributions scale with a power of the system size. In the mean-field universality class the skewness does not follow a power-law behavior and converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick model seem to be acceptably well fitted by a modified Gumbel distribution. Finally, we discuss the distribution of the internal energy of the Sherrington-Kirkpatrick model at finite temperatures and show that it behaves similar to the ground-state energy of the system if the temperature is smaller than the critical temperature.