Lattice Monte Carlo simulation and phase transitions in scalar field theories

Abstract

The cubic anisotropy model is a simple scalar field theory with a phase transition of either first- or second order depending on the values of its parameters, with similarities to the electroweak phase transition that occurred in the very early universe. Using lattice simulations, the critical mass of this phase transition is estimated for several values of the parameters, and an infinite volume estimate is produced. Further, the question of whether the phase transitions are first- or second order in the lattice model is investigated. The phase transitions are found to be of second-order when 3λ2/λ1 = 0,1,3, and first order when 3λ2/λ1 = 3.003, in line with existing theory on the matter.