The Two-Dimensional O(2) Model on a Random Planar Lattice at Strong Coupling

TL;DR

This paper investigates the strongly coupled 2D O(2) model on a random lattice, revealing solutions with gravity-like critical exponents and identifying an order parameter for the Kosterlitz--Thouless transition.

Contribution

It introduces a class of solutions for the model at large lattice spacings and links their critical behavior to pure 2D gravity, advancing understanding of phase transitions in random lattice models.

Findings

Solutions exhibit gravity-like critical exponents

Order parameter for Kosterlitz--Thouless transition identified

Critical behavior aligns with pure 2D gravity

Abstract

The large spacing phase of the infinite random matrix chain, which represents the strongly coupled two-dimensional O(2) model on a random planar lattice, is explored. A class of solutions valid for large lattice spacings is constructed. It is proved that these solutions exhibit the critical exponents characteristic of pure two-dimensional gravity. The character expansion for the chain model is developed and an order parameter governing the Kosterlitz--Thouless phase transition is identified.