Potts model partition functions on two families of fractal lattices

Helin Gong and Jin, Xian’an

Physica A: Statistical Mechanics and its Applications, 2014, vol. 414, issue C, 143-153

Abstract: The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.

Keywords: Potts model; Tutte polynomial; Spanning tree; Asymptotic growth constant; Connected spanning subgraph; The modified Koch graph (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:414:y:2014:i:c:p:143-153

DOI: 10.1016/j.physa.2014.07.047

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