6533b827fe1ef96bd1286453

RESEARCH PRODUCT

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

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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 $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ 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 $q=\ensuremath{\pi}$, 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.