ISING MODEL OVER CAYLEY LATTICES WITH LOCAL 2D GEOMETRY

摘要

A simple analysis of the thermodynamical properties of a hierarchical lattice with local 2D geometry is presented. The nonlinear maps that arise from the recursive procedure yield the thermodynamics of both the central (Bethe) region and of the complete lattice. In a particular limit, where the lattice collapses onto one with non-uniform coordination, a magnetic instability arises, preventing the appearance of a true second order transition. In the frustrated case, such an instability becomes marginally stable. [References: 12]