Chaos in the Z(2) Gauge Model on a Generalized Bethe Lattice of Plaquettes

We investigate the Z(2) gauge model on a generalized Bethe lattice with three plaquette representation of the action. We obtain the cascade of phase transitions according to Feigenbaum scheme leading to chaotic states for some values of parameters of the model. The duality between this gauge model and three site Ising spin model on Husimi tree is shown. The Lyapunov exponent as a new order parameter for the characterization of the model in the chaotic region is considered. The line of the second order phase transition, which corresponds to the points of the first period doubling bifurcation, is also obtained.Comment: LaTeX, 7 pages, 4 Postscript figure

The Phase Structure of Antiferromagnetic Ising Model in the Presence of Frustrations

The antiferromagnetic Ising model in a magnetic field is considered on the Husimi tree. Using iteration technique we draw the plots of magnetization versus external field for different temperatures and construct the resulting phase diagram. We show that frustration effects essentially change the critical properties. The model exhibits three distinct critical regions, including re-entrant phase structure and Griffiths singularities.Comment: 5 pages, 5 figures, submited to Phys. Lett.

Chaotic Repellers in Antiferromagnetic Ising Model

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at {\it positive} "temperature" $\beta_c = 0.89$. We obtain the density of the invariant measure on the chaotic repeller.Comment: LaTeX file, 10 pages, 4 PS figurs upon reques

Multisite antiferromagnetic Ising spin model: chaos in the description of chaotic repellers

This work was partly supported by the Grant-211-5291 YPI of the German Bundesministerium fur Forshung and Technologie and by the Grant INTAS-93-633Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal