The Rules Of Sub-critical Behavior Shaped Structure On The Spin Model System

In recent years the research on fractals has been an active field in the area of condensed matter physics. In particular, a great deal of attention has be.en paid to critical behaviors of fractals. The critical behaviors of classical spin system on some regular fractal lattices have been discussed in my thesis.The first a simple review on the recent progress in the subject had been made in chapter 1Chapter 2 investigates the Potts antiferromagnet situated on the fractal family of the diamond-type hierarchical lattices The exact analysis of our findings reveals that the algebraically ordered behavior predicted by Berker and Kadanoff can exist on such lattices with L=odd, where L is the structure parameter of the hierarchical lattices. However, the similar behavior to that of the antiferromagnetic Potts model on decorated square lattice is exhibited for the systems with L=even.The equvalences of the Ising model on hierarchical lattices having two- and four-site, and having two- and three-site couplings with the Ising model having only two-site interaction on the same lattice which are derived by a partial tracing can be found in chapter 3 and 4.We study how thermodynamic properties of the triplet interaction Ising model on a family of Sierpinski-type gasket fractals cross over to that of the Ising model on triangular lattice with three-spin interaction in half of the triangular faces, and the critical dynamics of the...