Quantitative behavior of (1,1/2)-MSIM on a Cayley tree

Abstract

In this paper, using the self-similarity technique, we establish the Gibbs measures related to the Ising model having mixed spin (1,1/2) (shortly, (1,1/2)-MSIM) on the semi-infinite Cayley tree (CT) and rigorously investigate the phase transition phenomena for (1,1/2)-MSIM on the CT by looking at the non-uniqueness of the fixed points for the relevant dynamic system. We demonstrate that the model displays chaotic behavior in some regions via the Lyapunov exponent. We compute the thermal average spin for the model. We present some exact formulas to calculate the free energy and entropy associated with (1,1/2)-MSIM on the second-order CT by employing the cavity technique.