论文标题
在二维液晶中缺乏列列准长范围，三个主管组件
Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
论文作者
论文摘要
Lebwohl-lasher模型描述了液晶中的各向同性纽扣过渡。在两个维度上，其连续对称性不能自发地破裂，自从数十年以来，它就经过数字进行了研究，特别是对拓扑过渡的猜想，导致具有准长范围的列前相。我们使用比例不变的散射理论来确切确定$ n $导演组件（$ rp^{n-1} $模型）的一般情况下的重新归一化组固定点，该点可产生$ n = 3 $的lebwohl-lasher模型。对于$ n> 2 $，我们显示了$ O（n（n+1）/2-1）$模型的通用类别中的零温度临界点的缺失以及零温度关键点。对于$ n = 2 $，固定点方程产生的berezinskii-kosterlitz-通信$ rp^1 \ sim o（2）$所需的无用过渡。
The Lebwohl-Lasher model describes the isotropic-nematic transition in liquid crystals. In two dimensions, where its continuous symmetry cannot break spontaneously, it is investigated numerically since decades to verify, in particular, the conjecture of a topological transition leading to a nematic phase with quasi-long-range order. We use scale invariant scattering theory to exactly determine the renormalization group fixed points in the general case of $N$ director components ($RP^{N-1}$ model), which yields the Lebwohl-Lasher model for $N=3$. For $N>2$ we show the absence of quasi-long-range order and the presence of a zero temperature critical point in the universality class of the $O(N(N+1)/2-1)$ model. For $N=2$ the fixed point equations yield the Berezinskii-Kosterlitz-Thouless transition required by the correspondence $RP^1\sim O(2)$.
