One-dimensional q-state Potts model with multi-site interactions

Abstract

A one-dimensional (1D) q-state Potts model with N sites, m-site interaction K in a field H is studied for arbitrary values of m. Exact results for the partition function and the two-point correlation function are obtained at H = 0. The system in a field is shown to be self-dual. Using a change of Potts variables, it is mapped onto a standard 2D Potts model, with first-neighbour interactions K and H, on a cylinder with helical boundary conditions (BC). The 2D system has a length and a transverse size m. Thus the Potts chain with multi-site interactions is expected to develop a 2D critical singularity along the self-duality line, , when and .