We determine the general structure of the partition function of the q-state Potts model in an external magnetic field, Z(G,q,v,w) for arbitrary q, temperature variable v, and magnetic field variable w, on cyclic, Möbius, and free strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices with width Ly and arbitrarily great length Lx. For the cyclic case we prove that the partition function has the form, where Λ denotes the lattice type, c̃(d) are specified polynomials of degree d in q, TZ,Λ,Ly,d is the corresponding transfer matrix, and m=Lx (Lx/2) for Λ=sq,tri (hc), respectively. An analogous formula is given for Möbius strips, while only TZ,Λ,Ly,d=0 appears for free strips. We exhibit a method for calculating TZ,Λ,Ly,d for arbitrary Ly and give illustrative examples. Explicit results for arbitrary Ly are presented for TZ,Λ,Ly,d with d=Ly and d=Ly-1. We find very simple formulas for the determinant det(TZ,Λ,Ly,d). We also give results for self-dual cyclic strips of the square lattice.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics