连续对称破缺时一阶跃迁的有限尺寸标度：三维XXZ海森堡反铁磁体中的自旋翻转跃迁
Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet
摘要：
利用高斯概率分布的一种近似方法，并引入一个唯象的“简并”因子，发展了连续对称性被破坏的一阶相变的有限尺寸标度。为了研究$L \times L \times L$简单立方晶格上类伊辛反铁磁态和倾斜类XY反铁磁态之间的一阶“自旋翻转”跃迁的有限尺寸行为，将预测结果与三维XXZ海森堡反铁磁场的蒙特卡罗模拟数据进行了比较。我们的理论预测，对于大的线性维数$L$的所有的序参量的时刻，以及四阶累积量的字段依赖表现出普遍的交叉。对前导顺序的更正应与反向体积成比例。在自旋翻转转变点处的这些交点的值可以用表征有序相的相对简并性的因子$q$来表示。我们的理论产量$q=π$，我们提出的数值证据，这是与此预测兼容。理论和模拟之间的协议意味着迄今未知的普遍性，可以调用一阶相变。
英文摘要：
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 $q=π$, 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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