The inverse spectral map for dimers

TL;DR

This paper presents an alternative rational-function-based method to invert the spectral transform for dimer cluster integrable systems, simplifying the process compared to previous theta function approaches.

Contribution

It introduces a new construction of the inverse spectral map for dimers using only rational functions, avoiding complex theta function calculations.

Findings

Provides a rational inverse map for the spectral transform

Simplifies the inversion process compared to previous methods

Enhances computational efficiency for spectral data analysis

Abstract

In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer cluster integrable system its spectral data, is birational by constructing an inverse map using theta functions on Jacobians of spectral curves. We provide an alternate construction of the inverse map that involves only rational functions in the spectral data.