N-vicinities method for 3D Ising Model
Abstract
The n-vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to the Ising model on the D-dimensional cubic lattice. The state equation is solved for an arbitrary dimension D and the behavior of the free energy is analyzed. For large values of D (D > 2) the obtained results are in good agreement with the ones obtained by means of computer simulations. For small values of D (D < 3), there are noticeable discrepancies with the exact results.
Keywords
Cite
@article{arxiv.1606.09034,
title = {N-vicinities method for 3D Ising Model},
author = {Boris Kryzhanovsky and Leonid Litinskii},
journal= {arXiv preprint arXiv:1606.09034},
year = {2016}
}
Comments
Slightly corrected version of the presentation on 5th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2016)