Statistical Mechanics Invited Talk

Koji Hukushima (University of Tokyo)

Equilibrium-state simulations of some (spin) glass models in finite dimensions

Mean-field theory of spin glasses has provided a number of novel concepts for understanding of a phase transition in disordered glassy systems. In particular, replica-symmetry breaking (RSB) plays an essential role in describing complex free-energy structure. It turns out that the pattern of RSB is clarified into two distinct classes, full RSB and one-step RSB. Despite extensive studies including large-scale numerical simulations, no conclusion has been reached about the issue whether the RSB concepts survive in short-ranged spin-glass models in finite dimensions. In recent years, some mean-field spin-glass models with the one-step RSB have attracted much attention of many researchers. These models are regarded as a prototype of a phenomenological picture of structural glass transition, called random first-order transition (RFOT), which is characterized by a thermodynamic transition with a discontinuous order parameter without latent heat. The advisability of the RSB picture in finite dimensional spin glass models comes to an issue again in the context of the structural glass transition. In this talk, we present some results of large-scale Monte Carlo simulations based on extended ensemble method for lattice glass model and Potts-glass model in finite dimensions. Our findings for the latter are fully compatible with those expected from the RFOT picture based on the one-step RSB.

An extended ensemble Monte Carlo study of a lattice glass model, K. Hukushima, S.Sasa, J. of Phys.: Conf. Ser., 233, 012004 (2010).