Spin-flop transition in the 3D anisotropic Heisenberg antiferromagnet: Finite size scaling for a first order transition where a continuous symmetry is broken

We use Monte Carlo simulations to explore the 3D anisotropic Heisenberg antiferromagnet in a field in order to study the finite size behavior of the first order “spin-flop” transition between the Ising-like antiferromagnetic state and the canted, XY-like state[1]. 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, q, included. Our theory yields q = π, and it 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. The values of these intersections at the spin-flop transition point can be expressed in terms of the factor q. Our theory and simulation imply a heretofore unknown universality can be invoked for first order phase transitions.

[1] S. Hu, S.-H. Tsai, and D. P. Landau, Phys. Rev. E 89, 032118 (2014)