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Spin glasses in the nonextensive regime.

Matthew Wittmann¹, A P Young

¹Department of Physics, University of California, Santa Cruz, California 95064, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 12, 2012

Summary

Monte Carlo simulations confirm that spin glasses in the nonextensive regime exhibit free energy matching infinite-range models. This finding holds for both one-dimensional and diluted long-range spin glasses.

Area of Science:

Condensed matter physics
Statistical mechanics

Background:

Spin systems with long-range interactions can exhibit nonextensivity.
A conjecture posits that in this regime, free energy equals that of infinite-range models.

Purpose of the Study:

To investigate the nonextensive regime of one-dimensional long-range spin glasses.
To test the conjecture regarding free energy equivalence to infinite-range models.
To explore analogous behavior in diluted long-range spin glasses.

Main Methods:

Monte Carlo simulations were employed.
Finite-size scaling analysis was used to determine transition temperatures.

Main Results:

Simulation results for transition temperatures are consistent with the conjecture for one-dimensional systems.

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Numerical evidence supports an analogous result for diluted long-range spin glasses.

Conclusions:

The free energy of nonextensive one-dimensional long-range spin glasses matches infinite-range models.
Diluted long-range spin glasses also exhibit this behavior, aligning with the Viana-Bray model.