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Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2005

## Fast Flat-Histogram Method for Generalized Spin Models

Sylvain Reynal
Hung-The Diep
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• PersonId : 828445

#### 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.

### Dates and versions

hal-00004708 , version 1 (14-04-2005)
hal-00004708 , version 2 (14-04-2005)
hal-00004708 , version 3 (06-10-2005)

### Identifiers

• HAL Id : hal-00004708 , version 3
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### Cite

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

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