Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet release_qpf5hy65xbhingmnwutgkdtova

Abstract

Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite size behavior on a L × L × L simple cubic lattice for the first order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension L the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor q that characterizes the relative degeneracy of the ordered phases. Our theory yields q=π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first order phase transitions.
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