2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21526We 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 TeXStatistical Mechanicstext