Monte Carlo simulation of two-dimensional flux-line-lattice melting

A Monte Carlo simulation of a two-dimensional flux-line-lattice (FLL) melting transition is presented. The internal energy, specific heat, Abrikosov ratio, and diffraction pattern of the magnitude {}{ψ}(x)² of the order-parameter field are calculated. By examining in detail the hysteresis, histogram, and relaxation profiles of the internal energy, the existence of a first-order phase transition is concluded. Below the transition temperature tₘ the diffraction pattern has six sharp peaks corresponding to the hexagonal symmetry of the triangular FLL, while it shows liquidlike behavior above tₘ. The sample-size dependence of the peak height clearly shows that the phase transition is the melting of the FLL. Comparison with earlier works is also made.