Universality-class dependence of energy distributions in spin glasses

Katzgraber HG, Körner M, Liers F, Jünger M, Hartmann AK (2005)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2005

Journal

Physical Review B American Physical Society

Publisher: American Physical Society

Book Volume: 72

Article Number: 094421

Journal Issue: 9

DOI: 10.1103/PhysRevB.72.094421

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. © 2005 The American Physical Society.

Authors with CRIS profile

Frauke Liers-Bergmann Professur für Optimization under Uncertainty & Data Analysis

Involved external institutions

Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich CH Switzerland (CH) Universität zu Köln DE Germany (DE) Carl von Ossietzky Universität Oldenburg DE Germany (DE)

How to cite

APA:

Katzgraber, H.G., Körner, M., Liers, F., Jünger, M., & Hartmann, A.K. (2005). Universality-class dependence of energy distributions in spin glasses. Physical Review B, 72(9). https://dx.doi.org/10.1103/PhysRevB.72.094421

MLA:

Katzgraber, Helmut G., et al. "Universality-class dependence of energy distributions in spin glasses." Physical Review B 72.9 (2005).

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