U(1)-gauged 2-flavor spin system in 3-D

TL;DR

This paper investigates a 3D U(1)-gauged 2-flavor spin system using Monte Carlo simulations, revealing a likely weakly first-order phase transition close to a multi-critical point, with implications for understanding gauge-spin interactions.

Contribution

It introduces a novel simulation approach for a constrained U(1)-gauged spin system and provides initial insights into its phase transition nature.

Findings

Indicates a second order phase transition driven by spin coupling.

Critical exponent inconsistent with conformal bootstrap constraints.

Transition likely weakly first order, near a multi-critical point.

Abstract

We study a U(1)-gauged 2-component spin system in 3 dimensions. For the gauge fields we use the Villain formulation with a constraint that removes lattice monopoles and in this form couple the gauge fields to 2-component spins. We discuss the simulation strategies for this highly constraint system and present first results for the phase structure. Our preliminary Monte Carlo simulations indicate that the system undergoes a second order phase transition driven by the spin coupling. However, the correlation length critical exponent is inconsistent with the conformal bootstrap constraint for a critical (rather than multi-critical) fixed point, which forces a conclusion that the transition is likely weakly 1st order, passing close to a multi-critical point. To reliably resolve the nature of the transition, simulations on larger lattices will be necessary.