格元轨道模型中长程序的真实性质
True nature of long-range order in a plaquette orbital model
摘要：
我们分析了最近由S。Wenzel和W.扬克在这个模型中，正方形晶格的边缘被划分为$x$和$z$ -两种类型，它们沿着两个坐标方向交替排列，从而排列成$x$和$z$ -格子的棋盘图案;然后经典O（2）-自旋通过它们在$x$ -边缘上的第一分量和通过它们在$z$ -边缘上的第二分量铁磁耦合。我们从第一性原理证明，在足够低的温度下，该模型表现出取向的长程序（OLRO）在两个主要的晶格方向之一。磁序被潜在的对称性所排除。一组类似的结果也推断出大自旋的量子系统，虽然$\frac12$实例目前似乎超出了严格的方法。我们指出，在数值模拟中观察到的元胞能量分布的Neél顺序是一个人工制品的OLRO和明智的选择的元胞能量。特别是，这种秩序似乎消失时，调整的元格能量消失在基态水平。我们还讨论了具体的作用，基本的对称性在Wenzel和Janke的模拟，并提出了一种增强的方法，可以在原则上显着提高收敛速度的数值采样。
英文摘要：
We analyze the classical version of a plaquette orbital model that was recently introduced and studied numerically by S. Wenzel and W. Janke. In this model, edges of the square lattice are partitioned into $x$ and $z$-types that alternate along both coordinate directions and thus arrange into a checkerboard pattern of $x$ and $z$-plaquettes; classical O(2)-spins are then coupled ferromagnetically via their first components over the $x$-edges and via their second components over the $z$-edges. We prove from first principles that, at sufficiently low temperatures, the model exhibits orientational long-range order (OLRO) in one of the two principal lattice directions. Magnetic order is precluded by the underlying symmetries. A similar set of results is inferred also for quantum systems with large spin although the $\frac12$ instance currently seems beyond the reach of rigorous methods. We point out that the Neél order in the plaquette energy distribution observed in numerical simulations is an artefact of the OLRO and a judicious choice of the plaquette energies. In particular, this order seems to disappear when the plaquette energies are adjusted to vanish at the ground-state level. We also discuss the specific role of the underlying symmetries in Wenzel and Janke's simulations and propose an enhanced method of numerical sampling that could in principle significantly increase the speed of convergence.
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