2024/10/29 by Chen, Yue, Shrock, Robert
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2410.22430
We present exact calculations of the q-state Potts model partition functions and the equivalent Tutte polynomials for chain graphs comprised of m repeated hammock subgraphs He1,...,er connected with line graphs of length eg edges, such that the chains have open or cyclic boundary conditions (BC). Here, He1,...,er is a hammock (series-parallel) subgraph with r separate paths along ``ropes'' with respective lengths e1, ..., er edges, connecting the two end vertices. We denote the resultant chain graph as G_\e1,...,er\,eg,m;BC. We discuss special cases, including chromatic, flow, and reliability polynomials. In the case of cyclic boundary conditions, the zeros of the Potts partition function in the complex q function accumulate, in the limit m → ∞, onto curves forming a locus \cal B, and we study this locus.