Exact Partition Functions for the $q$-State Potts Model with a Generalized Magnetic Field on Lattice Strip Graphs

Abstract

We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values $\{1,...,s\}$ with $s\le q$. For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product $S_s\otimes S_{q-s}$ global symmetry, where $S_s$ is the permutation group on $s$ objects.

23 pages

References in corpus (1)

• Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

Cited by in corpus (4)

• Calculating eigenvalues of many-body systems from partition functions
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Measures of Spin Ordering in the Potts Model with a Generalized External Magnetic Field