Six-Vertex, Loop and Tiling models: Integrability and Combinatorics

TL;DR

This paper reviews exactly solvable 2D statistical models like the six-vertex, loop, and tiling models, highlighting their integrability and applications in combinatorics and algebraic geometry.

Contribution

It synthesizes the author's work and related research on the integrability and combinatorial applications of these models.

Findings

Connections between solvable models and enumerative combinatorics

Applications to algebraic geometry

Overview of integrability in statistical models

Abstract

This is a review (including some background material) of the author's work and related activity on certain exactly solvable statistical models in two dimensions, including the six-vertex model, loop models and lozenge tilings. Applications to enumerative combinatorics and to algebraic geometry are described.