### Abstract

Original language | English |
---|---|

Article number | 066128 |

Journal | Physical Review E |

Volume | 70 |

DOIs | |

Publication status | Published - 22 Dec 2004 |

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### Bibliographical note

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*Physical Review E*,

*70*, [066128]. https://doi.org/10.1103/PhysRevE.70.066128

**Estimation of critical behavior from the density of states in classical statistical models.** / Malakis, A.; Peratzakis, A.; Fytas, Nikolaos.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 70, 066128. https://doi.org/10.1103/PhysRevE.70.066128

}

TY - JOUR

T1 - Estimation of critical behavior from the density of states in classical statistical models

AU - Malakis, A.

AU - Peratzakis, A.

AU - Fytas, Nikolaos

N1 - The full text is currently unavailable on the repository.

PY - 2004/12/22

Y1 - 2004/12/22

N2 - We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

AB - We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

U2 - 10.1103/PhysRevE.70.066128

DO - 10.1103/PhysRevE.70.066128

M3 - Article

VL - 70

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

M1 - 066128

ER -