Space Dependent Mean Field Approximation Modelling
It is shown that the self-consistency condition which is the basic equation for calculating the mean-field order parameter of any mean-field model Hamiltonian can be replaced by the standard Metropolis Monte Carlo scheme. The advantage of this method is its ease of implementation for both the homoge...
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Published in | Journal of statistical physics Vol. 154; no. 6; pp. 1508 - 1515 |
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Main Authors | , , , , , |
Format | Journal Article |
Language | English |
Published |
Boston
Springer US
01.03.2014
Springer |
Subjects | |
Online Access | Get full text |
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Summary: | It is shown that the self-consistency condition which is the basic equation for calculating the mean-field order parameter of any mean-field model Hamiltonian can be replaced by the standard Metropolis Monte Carlo scheme. The advantage of this method is its ease of implementation for both the homogeneous mean-field order parameter and the heterogeneous one. To be specific, the mean-field version of the Ising model spin system is discussed in detail and the resulting magnetization is the same as in the case of solving the respective mean-field self-consistency equation. In addition, it is shown that if a high temperature phase of such system is quenched below critical temperature then the mean field experienced by spins develops into a network of domains in analogous way as it happens with the spins in the case of the exact many-body Hamiltonian system and the coarsening processes start to take place. To show that the introduced Metropolis Monte Carlo method works also in case of the continuous variables the order parameter for the Maier-Saupe model for nematic liquid crystals has been calculated. |
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ISSN: | 0022-4715 1572-9613 |
DOI: | 10.1007/s10955-014-0944-8 |