Phase structure and critical behavior of multi-Higgs \(U(1)\) lattice gauge theory in three dimensions (Q1047688)

The paper investigates the three-dimensional \(U(1)\) gauge theory with multi-component Higgs fields having fixed amplitudes by using the Monte Carlo (MC) simulations. This model is of general interest and knowledge of its phase structure order of phase transitions, etc. may be useful to get better understanding of various physical systems, namely: \(N\)-component superconductor, p-wave superconductivity of cold Fermi gas, phase transition of 2D antiferromagnetic spin models, inflational cosmology and others. The paper considers the simplest form of the multi-Higgs lattice model, i. e. the 3D compact lattice gauge theory without Berry's phase. The Higgs fields are introduced on the site of the cubic lattice and treated in the London limit. The action is written via the Higgs coupling with its coefficients and the plaquette term with its coefficient. After the partition function of the model is given, a couple of the models based on these equations are investigated. For the MC simulations the standard Metropolis algorithm is used on the cubic lattice with the periodic boundary condition. First, the \(N = 2\) case with symmetric couplings is studied. There are measured the internal energy and the specific heat transitions. In this case, there is a critical line of second-order transitions in the gauge coupling - Higgs coupling plane, which distinguishes the Higgs phase and the confinement phase. The critical exponent of the phase transition obtained by means of the finite-size-scaling hypothesis is very close to that of the 3D XY-model. In 3D flavor Higgs model \((N = 3)\), there is a critical line similar to that in the \(N = 2\) case, but the critical line is separated into to parts one with first-order transitions and other with second-order transitions indicating the existence of a tricritical point. To study the mechanism of generation of these first-order transitions, the authors study the asymmetric cases and find two second-order transitions or one crossover and one second-order transition. The former case implies that two simultaneous second-order transitions strengthen the order to generate a first order transition. Finally, it is studied the symmetric case for \(N = 4\) and 5 multi-Higgs models at the zero gauge coupling.