Some New Exact Results for the q-State Potts Model on Ladder Graphs

Abstract

We present exact calculations of the partition function for the q-state Potts model for general q, temperature and magnetic field on strips of the square lattices of width $L_y=2$ and arbitrary length $L_x=m$ with periodic longitudinal boundary conditions. A new representation of the transfer matrix for the q-state Potts model is introduced which can be used to calculate the determinant of the transfer matrix for an arbirary $m\times m$ lattice with periodic boundary conditions.

8 pages TeX