Exact T = 0 partition functions for potts antiferromagnets on sections of the simple cubic lattice

Solutions were established for the zero-temperature partition of the q-state Potts antiferromagnet on tubes of the simple cubic lattice with various transverse cross sections and boundary conditions and with arbitrarily great length. These solutions were used to calculate, in the infinite-length limit, the resultant ground-state degeneracy per site W and the singular locus Β. In particular, the value of q_c of (q_c)_eff for these infinite-length tubes was calculated. The results show quantitatively how this quantity increases as the effective coordination number for a given family of graphs increases and are a step toward determining q_c is for the infinite simple cubic lattice.