Exact solution of d-dimensional ising model for finite continuous spins (D) and non-zero external field (B)

Kumar, N. (1972) Exact solution of d-dimensional ising model for finite continuous spins (D) and non-zero external field (B) Current Science, 41 (20). pp. 727-728. ISSN 0011-3891

[img]
Preview
PDF - Publisher Version
120kB

Official URL: http://cs-test.ias.ac.in/cs/Downloads/article_1556...

Abstract

Making use of the Stratonovich linearization procedure for bilinear exponents and certain eigenvalue properties of the generalised Jacobi matrices, an exact expression has been obtained, in a closed form, for the partition function of the d (=3) dimensional, nearest neighbour coupled, Ising model for "finite" continuous spins(=D) in the presence of an external field. A Gaussian measure has been chosen for integration over the spin space. The method admits complete generalisation with respect to the dimensionality, the range of interaction and the sign of the interaction constant J (ferro- or antiferromagnetic). All thermodynamical quantities of interest can be obtained by taking suitable partial derivatives of the partition function. The critical indices can be ascertained for the cases of d=3 for which the theory predicts a second-order phase transition. For the ferromagnetic case(J>0), the spontaneous magnetisation vanishes identically the temperature T>T (the transition temperarture) and the magnetic susceptibility follows essentially the Curie Weiss Law.

Item Type:Article
Source:Copyright of this article belongs to Current Science Association.
ID Code:85076
Deposited On:29 Feb 2012 11:54
Last Modified:19 May 2016 01:16

Repository Staff Only: item control page