Thermodynamics of multi-colored loop models in three dimensions

TL;DR

This paper investigates phase transitions in three-dimensional multi-colored loop models, revealing how symmetry and interactions influence whether the transitions are first or second order, with implications for related models like the XY model.

Contribution

It demonstrates the impact of inter-color interactions on the order of phase transitions and computes critical exponents for non-symmetric loops in 3D multi-colored loop models.

Findings

Symmetric loops undergo first-order transitions.

Non-symmetric loops exhibit second-order transitions with calculated exponents.

Inter-color interactions change the transition from continuous to discontinuous.

Abstract

We study order-disorder transitions in three-dimensional \textsl{multi-colored} loop models using Monte Carlo simulations. We show that the nature of the transition is intimately related to the nature of the loops. The symmetric loops undergo a first order phase transition, while the non-symmetric loops show a second-order transition. The critical exponents for the non-symmetric loops are calculated. In three dimensions, the regular loop model with no interactions is dual to the XY model. We argue that, due to interactions among the colors, the specific heat exponent is found to be different from that of the regular loop model. The continuous nature of the transition is altered to a discontinuous one due to the strong inter-color interactions.