COMPARATIVE MONTE-CARLO STUDY OF ISING SPIN-GLASSES IN 2 TO 5 DIMENSIONS

Monte Carlo simulations of the Edwards-Anderson-Ising spin glass with Gaussian distribution of nearest-neighbor exchange forces in four and five dimensions are performed to check the speculation that d=4 is the lower critical dimensionality. In contrast to this expectation we find no qualitative difference at all to the results in two and three dimensions. We still find that on not too long time-scales there is an apparently rather well defined freezing temperature Tf, where the susceptibility has a cusp, and below Tf nonzero order parameters q, ψ can be found as for d=2, 3. But even for d=5 the decay of the Edwards-Anderson order parameter below Tf is found to be consistent with a logarithmic variation over several decades of observation time. The possible interpretations of this result are discussed. Our data thus suggest that either there is no equilibrium phase transition in all these dimensions, or more likely that a phase transition exists for 2≦d≦5 but the properties of the 'ordered phase' may be rather peculiar. © 1979 Springer-Verlag.