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Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet
- Publication Year :
- 2019
-
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 $L \times L \times L$ 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 $q=\pi$, 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.<br />Comment: 20 pages, 21 figures
- Subjects :
- Physics - Computational Physics
Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1901.10643
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.99.023309