Abstract
We propose an improvement of a Monte Carlo method designed to treat the Ising model in a field [C. Lieu and J. Florencio, J. Low Temp. Phys. 89, 565 (1992)]. The method involves the counting of bonds linking neighboring like-spins and yields the degeneracy of the system's energy states, hence the partition function. There is no acceptance-rejection procedure and all the randomly generated configurations are kept. The sampling depends on geometry only, so results of a given run can be used for all temperatures and energy parameters. In order to understand the virtues and inadequacies of the method, we obtained exact results for small lattices. We find that a Monte Carlo run must be followed by a Gaussian fit in order to account properly for the rare events not recorded in the sampling. Finally, we also established bounds for the location of the peak for the specifc heat of the Ising model in a magnetic field in two dimensions for several values of the field in the thermodynamic limit.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
