Magnetic correlations in three-dimensional ising spin glasses

By a recursive method numerically exact free energies are calculated forL×L×M Ising lattices with random bonds andL=4, 4≦M≦10, applying free boundaries in the direction where the lattice is less small and otherwise periodic boundary conditions. Both for the±J model and the gaussian model the specific heat is in fair agreement with Monte Carlo results obtained for much larger lattices. However, the correlation function [〈S0SR〉T2]av is found to decay exponentially with distanceR [for 1≲R≦9] at temperatures far below the apparent freezing temperatures of the Monte Carlo simulations, implying that there is no nonzero Edwards-Anderson order parameter in equilibrium. This behavior is qualitatively different from Mattis spin glasses (or Ising ferromagnets) where even smaller lattices show pronounced magnetic order at low temperatures. As the Monte Carlo results give evidence for a nonzero Edwards-Anderson order parameter (for not too long observation times), which is fairly independent of lattice size down to sizes of 43, we suggest that Edwards-Anderson ordering is a nonequilibrium phenomenon visible only in studying dynamic properties.

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