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@article{faucris.123092024,
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.},
author = {Katzgraber, Helmut G. and Körner, Mathias and Liers, Frauke and Jünger, Michael and Hartmann, Alexander K.},
doi = {10.1103/PhysRevB.72.094421},
faupublication = {no},
journal = {Physical Review B},
peerreviewed = {Yes},
title = {{Universality}-class dependence of energy distributions in spin glasses},
volume = {72},
year = {2005}
}