Universality-class dependence of energy distributions in spin glasses

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.

15 pages, 20 figures, 1 table

References in corpus (7)

• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo
• Universality in the level statistics of disordered systems
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Clustering analysis of the ground-state structure of the vertex-cover problem
• Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass

Cited by in corpus (14)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension $d=1,2,3$ via a Monte-Carlo procedure in the disorder
• Probing tails of energy distributions using importance-sampling in the disorder with a guiding function
• One-dimensional infinite component vector spin glass with long-range interactions
• Local field distributions in spin glasses
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Finding Ground States of Sherrington-Kirkpatrick Spin Glasses with Hierarchical BOA and Genetic Algorithms
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass
• A Monte Carlo Algorithm for Sampling Rare Events: Application to a Search for the Griffiths Singularity
• Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Analysis of Evolutionary Algorithms on the One-Dimensional Spin Glass with Power-Law Interactions