A comment on the solutions of the generalized Faddeev-Volkov model

TL;DR

This paper compares two recent generalizations of the exactly solvable Faddeev-Volkov lattice model, showing that their weight functions are essentially equivalent despite different construction methods.

Contribution

It demonstrates the equivalence of two distinct approaches to generalizing the Faddeev-Volkov model, unifying their weight functions up to a constant.

Findings

The weight functions from both models are the same up to a constant.

Different techniques yield equivalent generalized models.

The models extend the solvability of the original Faddeev-Volkov model.

Abstract

We consider two recent generalizations of the Faddeev-Volkov model, which is exactly solvable Ising-type lattice spin model. The first generalization based on using of the non-compact quantum dilogarithm over Pontryagin self-dual LCA group $\mathbb{R}\times \mathbb{Z}/N\mathbb{Z}$, and another one constructed in a recent study via the gauge/YBE correspondence. We show that weight functions of these models obtained by different techniques are the same up to a constant.