REDUCED TRANSFER MATRIX APPROACH FOR ISING MODEL

Kaya T., Arık M.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, vol.25, pp.2895-2903, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25
  • Publication Date: 2011
  • Doi Number: 10.1142/s0217979211101235
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS B
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2895-2903
  • Keywords: Classical statistical mechanics, classical spin models, lattice theory and statistics, MOLECULAR-FIELD THEORY, RENORMALIZATION-GROUP, FERROMAGNET, STATISTICS, CRYSTALS
  • Yıldız Technical University Affiliated: Yes

Abstract

In this work, we present a simple approximate transfer matrix method for 2D and 3D Ising ferromagnet to calculate spontaneous magnetization of the system. The critical coupling strength K-c of 2D and 3D Ising models in reduced transfer matrix approximation is obtained quite accurately by simple improvements over the mean field theory. The important physical effect we include is the some of the fluctuations effects of the systems directly with help of this method. We predict from the spontaneous magnetization curve that the critical coupling strength K-c = J/k(B)T = 0.401 and 0.245 for two-dimensional (2D) and three-dimensional (3D) systems, respectively.