n-vicinities method for three dimensional Ising Model

5th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Kryzhanovsky, Boris^1 ; Litinskii, Leonid^1

Scientific Research Institute for System Analysis of Russian Academy of Science, Nakhimovskii prospect Str. 36-1, Moscow

117218, Russia^1

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

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012064/pdf
DOI  :  10.1088/1742-6596/738/1/012064

来源: IOP

【 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.