The Rotor Model with spectral parameters and enumerations of Alternating Sign Matrices

TL;DR

This paper analyzes the Rotor Model with spectral parameters, using integrability and polynomiality to connect it to Alternating Sign Matrices, providing new sum rules and enumerations.

Contribution

It introduces spectral parameters into the Rotor Model and links it to Alternating Sign Matrices through integrability and polynomial analysis.

Findings

Derived sum rules for the Rotor Model

Connected the model to 3-enumerations of Alternating Sign Matrices

Identified maximally nested components under various boundary conditions

Abstract

In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us to determine the sum rule and a family of maximally nested components for different boundary conditions. We see in this way the appearance of 3-enumerations of Alternating Sign Matrices.