Phase transitions and composite order in $\mathrm{U}(1)^N$ lattice London models

TL;DR

This paper investigates phase transitions in multicomponent U(1)^N lattice models, revealing the nature of discontinuities and the emergence of a composite order phase for N up to 7, with implications for understanding complex gauge theories.

Contribution

It provides a quantitative analysis of the discontinuity of phase transitions in U(1)^N models and identifies a new composite order phase at higher coupling strengths.

Findings

Transition is discontinuous for N ≤ 7.

A new phase with composite order appears at higher coupling.

Discontinuous transitions are linked to van der Waals-type interactions.

Abstract

The phase diagrams and the nature of the phase transitions in multicomponent gauge theories with an Abelian gauge field are important topics with various physical applications. While an early renormalization-group-based study indicated that the direct transition from a fully ordered to a fully disordered state is continuous for $N = 1$ and $N > 183$, recently it was demonstrated that the transition is discontinuous for $N = 2$. We quantitatively study the dependence on $N$ of the degree of discontinuity of this transition. Our results suggest that the transition is discontinuous at least up to $N = 7$. Furthermore, we demonstrate that, at increased coupling strength, the phase transitions of the neutral and charged sectors of the model split, which for $N > 2$ yields a new phase with composite order. The transition from the composite-order phase to the fully disordered phase is then also discontinuous, at least for $N = 3$ and $N = 4$. Via a duality argument, this indicates that van der Waals-type interaction between directed loops may be responsible for the discontinuous phase transitions in these models.