Understanding principles of critical exponents and Universality at 2nd order phase transitions was a triumph of late 20th century physics. In contrast, 1st order transitions appeared to be boring. We will show how Monte Carlo simulations, together with experiment and theory, reveal unexpected behavior at a 1st order phase transition. To do this we examine the 1st-order “spin-flop” transition between the Ising-like antiferromagnetic state and the canted, XY-like state found in many anisotropic antiferromagnetic materials. Finite-size scaling for a 1st-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions. Predictions are compared with data from Monte Carlo simulations of an anisotropic Heisenberg antiferromagnet in a magnetic field. Our theory predicts that for large linear dimension the field dependence of all moments of the order parameters as well as the 4th-order cumulants exhibit universal intersections that can be expressed in terms of a factor q that characterizes the relative degeneracy of the ordered phases. Our theory yields simply q = π, independent of temperature!, and the agreement with numerical data implies a heretofore unknown Universality for 1st-order phase transitions.
Thursday, August 27, at 3:55PM.
