Kosterlitz Thouless Universality in Dimer Models

TL;DR

This paper demonstrates that certain lattice gauge theories in 2+1 dimensions undergo finite temperature phase transitions in the Kosterlitz-Thouless universality class, unaffected by large N limits, challenging mean field assumptions.

Contribution

It introduces a new cluster algorithm enabling precise analysis of phase transitions in monomer-dimer models, establishing their Kosterlitz-Thouless universality class.

Findings

Finite temperature phase transition in these models is of Kosterlitz-Thouless type.

Universality class remains unchanged even at large N.

Mean field analysis fails in the critical region.

Abstract

Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that this universality class is unaffected even in the large N limit. This shows that the mean field analysis often used in this limit breaks down in the critical region.