Exact Renormalization Group Exhibiting a Tricritical Fixed Point for a Spin-1 Ising Model in One Dimension

Abstract

Exact renormalization-group recursion relations are studied for a spin-1 Ising model in one dimension. In this model, critical lines are marked by a double degeneracy of the largest eigenvalue of the transfer matrix, and the tricritical point by a triple degeneracy. This is directly related to the tricritical fixed point being more unstable than the critical fixed points.