On the equivalence between stochastic baker's maps and two-dimensional spin systems

Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology 412 96 Göteborg, Sweden, EU

Corresponding author: kristian.lindgren@chalmers.se

Received: 5 March 2010
Accepted: 3 May 2010

Abstract

We show that there is a class of stochastic bakers transformations that is equivalent to the class of equilibrium solutions of two-dimensional spin systems with finite interaction. The construction is such that the equilibrium distribution of the spin lattice is identical to the invariant measure in the corresponding bakers transformation. We illustrate the equivalence by deriving two stochastic bakers maps representing the Ising model at a temperature above and below the critical temperature, respectively. A calculation of the invariant measure and the free energy in the baker system is then shown to be in agreement with analytic results of the two-dimensional Ising model.