Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces

TL;DR

This paper investigates phase transitions in a model of random matrices on discretized surfaces, revealing an infinite series of transitions at specific lattice spacings and developing methods to analyze these phenomena.

Contribution

It introduces a novel analysis of phase transitions in random matrix models on discretized surfaces, including an infinite series of special transitions and a new analytical approach.

Findings

Discovery of an infinite series of phase transitions at specific lattice spacings

Development of a method to analyze transition regions and determine critical exponents

Proposition that vortex-curvature interactions induce these phase transitions

Abstract

The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at special values of the lattice spacing \epsilon_{pq}=\sin(\pi p/2q). An unusual property of these transitions is that they are totally invisible in the double scaling limit. A method which allows us to explore the transition regions analytically and to determine certain critical exponents is developed. It is argued that phase transitions of this kind can be induced by the interaction of two-dimensional vortices with curvature defects of a fluctuating random lattice.