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Europhysics Letters (EPL)

Dynamical Behaviour of Three-Dimensional Ising Spin Glasses

Nicolas Sourlas

Published Feb 15, 1986• 18 citations
Publisher

Abstract

We present the results of a numerical simulation of a three-dimensional nearest-neighbour J = ± 1 Ising spin glass model, and show strong evidence for the existence of many states at low temperature. The internal energy, the magnetization and the Edwards-Anderson order parameter are found to be self-averaging and state independent, while characteristic times are not. We also find strong evidence for 1/ f magnetic noise.

DOI
10.1209/0295-5075/1/4/006

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We present the results of a numerical simulation of a three-dimensional nearest-neighbour J = ± 1 Ising spin glass model, and show strong evidence for the existence of many states at low temperature. The internal energy, the magnetization and the Edwards-Anderson order parameter are found to be self-averaging and state independent, while characteristic times are not. We also find strong evidence for 1/ f magnetic noise.
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.
We present numerical simulations of the four-dimensional Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite-size effects, suggest the existence of a spin-glass phase transition. We present a preliminar determination of critical exponents. We discuss spin-glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite-size effects, and the behaviour of the disorder-dependent and integrated probability distributions.
We characterize numerically the properties of the phase transition of the three-dimensional Ising spin glass with Gaussian couplings and of the low-temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses.
The Edwards and Anderson model (1975) for spin glasses is investigated by a real space rescaling transformation on an S= 1 / 2 Ising Hamiltonian with nearest-neighbour-only interactions in three dimensions. A transition to a spin glass ordered phase is found at about half the mean transition temperature, in contrast to earlier work on a two-dimensional model where no transition was found. The results suggest that the lower critical dimensionality, d c , for spin glass order is slightly greater than 2, although possibly d c =2 exactly. The specific heat is calculated and found to exhibit a broad maximum above T c , with no discernable singularity at the transition since the exponent alpha is large and negative.