Spin glasses in the nonextensive regime

Abstract

Spin systems with long-range interactions are "nonextensive" if the strength of the interactions falls off sufficiently slowly with distance. It has been conjectured for ferromagnets and, more recently, for spin glasses that, everywhere in the nonextensive regime, the free energy is exactly equal to that for the infinite range model in which the characteristic strength of the interaction is independent of distance. In this paper we present the results of Monte Carlo simulations of the one-dimensional long-range spin glasses in the nonextensive regime. Using finite-size scaling, our results for the transition temperatures are consistent with this prediction. We also propose and provide numerical evidence for an analogous result for dilutedlong-range spin glasses in which the coordination number is finite, namely, that the transition temperature throughout the nonextensive regime is equal to that of the infinite-range model known as the Viana-Bray model.