Tricritical points in a compact $U(1)$ lattice gauge theory at strong coupling

TL;DR

This paper explores how adding a higher derivative term to a compact U(1) lattice gauge theory can change the phase transition from first order to continuous, revealing tricritical points that may allow a nontrivial continuum limit.

Contribution

It introduces a higher derivative term to the lattice gauge theory, enabling continuous phase transitions and the emergence of tricritical points at strong coupling.

Findings

Existence of a continuous transition at strong coupling with the HD term.

Identification of tricritical points as potential nontrivial continuum limits.

Transition changes from first order to continuous with increasing HD term coefficient.

Abstract

Pure {\it compact} $U(1)$ lattice gauge theory exhibits a phase transition at gauge coupling $g \sim {\cal{O}}(1)$ separating a familiar weak coupling Coulomb phase, having free massless photons, from a strong coupling phase. However, the phase transition was found to be of first order, ruling out any nontrivial theory resulting from a continuum limit from the strong coupling side. In this work, a compact $U(1)$ lattice gauge theory is studied with addition of a dimension-two mass counterterm and a higher derivative (HD) term that ensures a unique vacuum and produces a covariant gauge-fixing term in the naive continuum limit. For a reasonably large coefficient of the HD term, now there exists a continuous transition from a regular ordered phase to a spatially modulated ordered phase. For weak gauge couplings, a continuum limit from the regular ordered phase results in a familiar theory consisting of free massless photons. For strong gauge couplings with $g\ge {\cal{O}}(1)$, this transition changes from first order to continuous as the coefficient of the HD term is increased, resulting in tricritical points which appear to be a candidate in this theory for a possible nontrivial continuum limit.