论文标题
具有随机定向晶体的XY模型中的相变
Phase transitions in XY models with randomly oriented crystal fields
论文作者
论文摘要
我们在完全连接的图上获得了XY模型的自由能的表示，其旋转受到强度$ D $的随机晶体和随机取向$α$。对于任何$ d $，可以使用大偏差理论获得该疾病的任意概率分布的结果。我们表明，对于包括四倍体分布的大家庭，临界温度对分布$ p（α）$的性质和强度不敏感，其中包括$ p（α+\fracπ{2}）$，其中包括均匀和对称的bimodal分布。特定的热量随着温度$ t \ rightarrow 0 $而消失，如果$ d $是无限的，但是如果$ d $是有限的，则接近恒定。 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.所有有限的$ d $都存在倾斜的混合阶段，但是当$ d \ rightarrow \ infty $时会消失。
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 $D \rightarrow \infty$.
