Spin glasses in the non-extensive regime

Abstract

Spin systems with long-range interactions are "non-extensive" 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 non-extensive 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 non-extensive 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 diluted long-range spin glasses in which the coordination number is finite, namely that the transition temperature throughout the non-extensive regime is equal to that of the infinite-range model known as the Viana-Bray model.

8 pages; corrected typos, additional background and references relating to FSS corrections

References in corpus (3)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

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