The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics

TL;DR

This paper explores the Razumov-Stroganov conjecture, revealing a deep link between statistical mechanics and combinatorics through stochastic processes, lattice models, and supersymmetry, highlighting recent advances and explanations.

Contribution

It clarifies the connection between physical eigenstates and combinatorial objects, building on recent work by Zinn-Justin and Di Francesco.

Findings

Establishes the link between eigenstates and combinatorics

Explains recent developments in the conjecture

Highlights the interdisciplinary nature of the research

Abstract

A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco.