Evidence for the double degeneracy of the ground-state in the 3D $\pm J$ spin glass

Abstract

A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional $\pm J$ Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations. The principal advantage of this version of the multicanonical method, however, was its ability to access information predictive of low-temperature behavior. At low temperatures we found results on the three-dimensional $\pm J$ Ising spin glass consistent with a double degeneracy of the ground-state: the order-parameter distribution function $P(q)$ converged to two delta-function peaks and the Binder parameter approached unity as the system size was increased. With the same density of states used to compute these properties at low temperature, we found their behavior changing as the temperature is increased towards the spin glass transition temperature. Just below this temperature, the behavior is consistent with the standard mean-field picture that has an infinitely degenerate ground state. Using the concept of zero-energy droplets, we also discuss the structure of the ground-state degeneracy. The size distribution of the zero-energy droplets was found to produce the two delta-function peaks of $P(q)$.

33 pages with 31 eps figures included

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Cited by in corpus (8)

• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Which measures of spin-glass overlaps are informative?
• The cumulative overlap distribution function in realistic spin glasses
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Nature of spin glass order in physical dimensions
• Finite-Size Scaling in the Energy-Entropy Plane for the 2D +- J Ising Spin Glass