Eur. Phys. J. B (2012) 85: 99
https://doi.org/10.1140/epjb/e2012-10625-7

Regular Article

Potts model on recursive lattices: some new exact results

¹ Centro de Estudios Científicos (CECS), 5110466 Valdivia, Chile
² Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, 22 Santiago, Chile

^a e-mail: alvarez@cecs.cl
^b e-mail: canfora@cecs.cl
^c e-mail: sreyes@fis.puc.cl

Received: 19 December 2011
Published online: 21 March 2012

Abstract

We compute the partition function of the Potts model with arbitrary values of q and temperature on some strip lattices. We consider strips of width L_y = 2, for three different lattices: square, diced and ‘shortest-path’ (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths L_y = 2,3,4,5. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width L_y = 3 and L_y = m + 2, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.