二维耦合三面体模型中手征有序的热破坏
Thermal destruction of chiral order in a two-dimensional model of coupled trihedra
摘要：
我们引入了一个极小模型来描述经典的二维受抑海森堡系统的物理，其中自旋在T=0时以非平面的方式排列。该模型由耦合三面体（或Ising- $\mathbb{R}P^3$模型）组成，包含Ising（手征）自由度、自旋波激发和$\Z_2$涡旋。广泛的蒙特卡罗模拟表明，T=0手征顺序消失在有限的温度下，在一个连续的相变的二维伊辛普适类，尽管误导的中间尺寸的影响，在过渡。组态分析表明，短程自旋涨落和$\Z_2$涡旋扩散的手征畴壁附近解释了强重整化的转变温度。手性域壁本身可以携带非定域的$\Z_2$拓扑电荷，并且涡旋然后优先与带电壁配对。此外，我们推测，反常的尺寸效应表明本模型接近三临界点。一个机构的结果，都支持这一主张：（i）在几个相关模型上通过蒙特卡罗模拟获得的一级跃迁（ii）Ising- $\mathbb{R}P^3$模型和稀伊辛模型之间的近似映射（表现出一个三临界点），最后，（iii）平均场的结果得到伊辛多自旋哈密顿，从Ising- $\mathbb{R}P^3$模型的矢量自旋的高温展开导出。
英文摘要：
We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a non-planar way at T=0. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}P^3$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations and $\Z_2$ vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and $\Z_2$ vortices proliferate near the chiral domain walls explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized $\Z_2$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size-effects suggest the proximity of the present model to a tricritical point. A body of results is presented, that all support this claim: (i) First-order transitions obtained by Monte Carlo simulations on several related models (ii) Approximate mapping between the Ising-$\mathbb{R}P^3$ model and a dilute Ising model (exhibiting a tricritical point) and, finally, (iii) Mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}P^3$ model.
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