Evidence for the double degeneracy of the ground state in the three-dimensional±Jspin glass

Abstract

A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional ±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 ±J Ising spin glass consistent with a double degeneracy of the groundstate: 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).

A new approach to Monte Carlo simulations in statistical physics

“…It is possible to heat the system to increase the possibility of escape from local minima by simulated annealing and the more recent simulated tempering method [61] and parallel tempering method [62,63], but it is still very difficult to reach equilibrium at low temperatures. Recently Hatano and Gubernatis proposed a bivariate multicanonical Monte Carlo method for the 3D ±J spin glass model, and their result also favors the droplet picture [16,64]. Marinari et al argued, however, that the data were not thermalized [58].…”

Influence of uniaxial anisotropy on a quantumXYspin-glass model with ferromagnetic coupling

“…Recently, a large number of experimental and theoretical studies on the spin glasses have been obtained. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] These works focus their attentions on the aging, 25,26 the memory, 27,28 the nonequilibrium dynamics, 29,30 and Griffiths singularities, 31 even on the nonlinear response. 32,33 As is known, various anisotropies play important roles in the spin glass systems.…”

Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass

“…This is especially true because essentially all of the work on three-dimensional (3D) EA models at low temperatures must be done on lattices with L ≤ 20, due to our inability to equilibrate larger lattices at low temperatures in 3D. 13 At least one example of complex behavior of the order parameter emerging as L is increased is already known in a similar 3D model. 14 In this work we will analyze data for the energies and entropies of the ground states (GS) of 2D Ising spin glasses obtained using methods from earlier work.…”