Applicability of n-vicinity method for calculation of free energy of Ising model

Boris Kryzhanovsky and Leonid Litinskii

Physica A: Statistical Mechanics and its Applications, 2017, vol. 468, issue C, 493-507

Abstract: Here we apply the n-vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D-dimensional hypercube lattice. We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy. As expected, for large dimensions (D≥3) the system demonstrates a phase transition of the second kind. In this case, we obtain a simple analytical expression for the critical value of the inverse temperature. When 3≤D≤7 this expression is in a very good agreement with the results of computer simulations. In the case of small dimensions (D=1,2), there is a noticeable discrepancy with the known exact results.

Keywords: Partition function; Normal distribution; Ising model; Critical temperature (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437116307786
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:468:y:2017:i:c:p:493-507

DOI: 10.1016/j.physa.2016.10.074

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().