n-vicinities method for three dimensional Ising Model

[摘要] 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, there are noticeable discrepancies with the exact results.

[发布机构] Scientific Research Institute for System Analysis of Russian Academy of Science, Nakhimovskii prospect Str. 36-1, Moscow; 117218, Russia^1

[效力级别] 数学

[关键词] Approximate calculations;Arbitrary dimension;Cubic lattice;Equation of state;Exact results;Partition functions;State equations;Three-dimensional Ising model