Some remarks on a generalization of the superintegrable chiral Potts model

TL;DR

This paper generalizes a conjecture about expressing the partition function of the superintegrable chiral Potts model as a determinant, extending it to Hamiltonians satisfying a broader Onsager algebra.

Contribution

It extends the determinant representation conjecture for the partition function to a wider class of Hamiltonians obeying a generalized Onsager algebra.

Findings

Conjecture that W can be expressed as a determinant for a broader class of Hamiltonians.

Proposed a conjecture for the elements of the central spin operator S.

Generalized the previous determinant representation to models with more general algebraic structures.

Abstract

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced hamiltonians H and a central spin operator S. We conjectured in a previous paper that W can be written as a determinant, similar to that of the Ising model. Here we generalize this conjecture to any Hamiltonians that satisfy a more general Onsager algebra, and give a conjecture for the elements of S.