# Fast Flat-Histogram Method for Generalized Spin Models

Abstract : We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random-walk in the energy space with collective updates controlled by the microcanonical temperature, our method yields dynamic exponents close to their ideal random-walk values, reduced equilibrium times, and very low statistical error on the density of states. The method can host any density of states estimation scheme, including the Wang-Landau algorithm and the transition matrix method. Our approach proves remarkably powerful in the numerical study of models governed by long-range interactions, where it is shown to reduce the algorithm complexity to that of a short-range model with the same number of spins. We apply the method to the $q$-state Potts chains $(3\\leq q \\leq 12)$ with power-law decaying interactions in their first-order regime; we find that conventional local-update algorithms are outperformed already for sizes above a few hundred spins. By considering chains containing up to $2^{16}$ spins, which we simulated in fairly reasonable time, we obtain estimates of transition temperatures correct to five-figure accuracy. Finally, we propose several efficient schemes aimed at estimating the microcanonical temperature.
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Journal articles

https://hal.archives-ouvertes.fr/hal-00004708
Contributor : Sylvain Reynal <>
Submitted on : Thursday, October 6, 2005 - 6:07:59 PM
Last modification on : Thursday, May 3, 2018 - 3:18:02 PM
Long-term archiving on : Thursday, September 23, 2010 - 3:48:02 PM

### Citation

Sylvain Reynal, Hung-The Diep. Fast Flat-Histogram Method for Generalized Spin Models. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2005, 72, pp.056710. ⟨10.1103/PhysRevE.72.056710⟩. ⟨hal-00004708v3⟩

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