Order parameters forn-vector spin glasses ind dimensions

Abstract

We report Monte Carlo simulations of the time-dependent behavior of Edwards-Anderson spin glasses with Gaussian nearest-neighbor exchange, for both spin dimensionalityn and space dimensionalityd from 2 up to 6. A (nearly) logarithmic decay of the Edwards-Anderson order parameter with time is observed for alln and alld, similar to earlier studies forn=1. But the Monte Carlo data forn>1 suggest stronger than those forn=1 that all order parameters considered vanish in thermal equilibrium for nonzero temperature, because the decay forn>1 is faster at the temperatures of interest. For Heisenberg spins (n=3) no significant dependence of the Edwards-Anderson order parameterq on the size of the lattice was observed ford=2,3 and 4, whereas ford=5 and 6,q was smaller for smaller systems (in contrast to thed=5 Ising case). These results are the first Monte Carlo indication of a change in the bulk behavior of Heisenberg spin glasses at dimensionalityd=4. Quenching the system to zero temperature and then applying a field we find that the order parameter ψ, measuring the alignment with respect to the state at zero field, is destroyed by a sufficiently strong magnetic field, for all observedn andd.