具有随机取向晶场的XY模型的相变
Phase transitions in XY models with randomly oriented crystal fields
摘要：
我们得到了XY模型的自由能表示在一个完全连通的图与自旋受到一个随机晶体场的强度$D$和随机取向$α$。结果得到任意概率分布的障碍，使用大偏差理论，任何$D$。我们表明，临界温度是不敏感的性质和强度的分布$p(α)$，一个大家庭的分布，其中包括四周期分布，与$p(α)=p(α+\fracπ{2})$，其中包括均匀和对称的双峰分布。如果$D$无限大，比热随温度$T \rightarrow 0$而消失，但如果$D$有限大，则接近常数。我们还研究了非对称性对随机晶场取向双峰分布的影响，得到了包含四个相的相图：混合相（其中自旋以取决于无序度的角度倾斜）、$x$ -Ising相、$y$ -Ising相和顺磁相，它们都在四临界点相遇。对于所有的有限$D$，斜交混合相都存在，但对于$D \rightarrow \infty$，斜交混合相消失.
英文摘要：
We obtain a representation of the free energy of an XY model on a fully connected graph with spins subjected to a random crystal field of strength $D$ and with random orientation $α$. Results are obtained for an arbitrary probability distribution of the disorder using large deviation theory, for any $D$. We show that the critical temperature is insensitive to the nature and strength of the distribution $p(α)$, for a large family of distributions which includes quadriperiodic distributions, with $p(α)=p(α+\fracπ{2})$, which includes the uniform and symmetric bimodal distributions. The specific heat vanishes as temperature $T \rightarrow 0$ if $D$ is infinite, but approaches a constant if $D$ is finite. We also studied the effect of asymmetry on a bimodal distribution of the orientation of the random crystal field and obtained the phase diagram comprising four phases: a mixed phase (in which spins are canted at angles which depend on the degree of disorder), an $x$-Ising phase, a $y$-Ising phase and a paramagnetic phase, all of which meet at a tetra-critical point. The canted mixed phase is present for all finite $D$, but vanishes when $D \rightarrow \infty$.
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