Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-12-23
Physics
Condensed Matter
Statistical Mechanics
17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples add
Scientific paper
By repeated application of the deletion-contraction identity we compute the partition function of the Potts model on lattices with recursive symmetry with arbitrary values of $q$ and temperature parameter $v=e^K-1$. We first apply the technique to analyze strips of width $L_y=2$, for three different lattices: square, kagom\'e and `shortest-path' (to be defined in the text). It is shown that this approach is not restricted to the explicitly solved lattices, but can be applied to a very broad family of graphs of finite width constructed with an arbitrary number of recursive steps. Additionally, we show that the same procedure can be applied to wider strips by solving the kagom\'e strip of width $L_y=5$ with the aid of a computer program. As a demonstration of the versatility of the method we construct the exact solution of a recursive lattice similar to strips but whose width changes periodically from $L_y=3$ to $L_y=m$, where $m$ is an arbitrary integer number. Lastly, we analyze a non-periodic lattice for which the transfer matrix becomes step-dependent
Alvarez Pedro D.
Canfora Fabrizio
Reyes Sebastian A.
Riquelme Simon
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