Universality-class dependence of energy distributions in spin glasses
| dc.creator | Katzgraber, Helmut G. | |
| dc.creator | Koerner, Mathias | |
| dc.creator | Liers, Frauke | |
| dc.creator | Juenger, Michael | |
| dc.creator | Hartmann, A. K. | |
| dc.date | 2005-06-09 | |
| dc.date | 2005-09-18 | |
| dc.date.accessioned | 2026-07-07T06:27:18Z | |
| dc.date.available | 2026-07-07T06:27:18Z | |
| dc.description | 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. | |
| dc.description | 15 pages, 20 figures, 1 table | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0506209 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0506209 | |
| dc.identifier | Phys. Rev. B 72, 094421 (2005) | |
| dc.identifier | doi:10.1103/PhysRevB.72.094421 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97381 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Universality-class dependence of energy distributions in spin glasses | |
| dc.type | text |