Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.