Thermodynamics of multicolored loop models in three dimensions

We study order-disorder transitions in three-dimensional multicolored 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 nonsymmetric loops show a second-order transition. The critical exponents for the nonsymmetric 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 intercolor interactions.