The antiferromagnetic XY model on the triangular lattice: topological singularities

The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling

We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice. The system is fully frustrated and displays two families of ground states distinguished by the chirality of the spin field. We compute the Γ-limit of the energy in a regime which detects chirality transitions on one-dimensional interfaces between the two admissible chirality phases.

Conjectures on spectral numbers for upper triangular matrices and for singularities

Cecotti and Vafa proposed in 1993 a beautiful idea how to associate spectral numbers $α_1,...,α_n\in{\mathbb R}$ to real upper triangular $n\times n$ matrices $S$ with 1's on the diagonal and eigenvalues of $S^{-1}S^t$ in the unit sphere. Especially, $\exp(-2πiα_j)$ shall be the eigenvalues of $S^{-1}S^t$. We tried to make their idea rigorous, but we succeeded only partially. This paper fixes our results and our conjectures. For certain subfamilies of matrices their idea works marvellously, and there the spectral numbers fit well to natural (split) polarized mixed Hodge structures. We formulat…

反铁磁Potts模型III的传递矩阵和配分函数零点。三角格色多项式

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial

本文研究了m个\times n个三角网格条的色多项式P_G（q），其宽度m <= 12_P，9_F（分别具有周期性或自由横向边界条件）和任意长度n（具有自由纵向边界条件）。色多项式给出了q态Potts反铁磁体的配分函数的零温度极限。我们计算的转移矩阵的Fortuin-Kasteleyn表示，并获得相应的累积集的色零点在复q平面上的极限n \to \infty。我们重新计算的极限曲线巴克斯特在热力学极限m，n \to \infty，并找到新的有趣的功能与可能的物理后果。最后，我们分析了孤立极限点及其与Beraha数的关系。

低维晶格上反铁磁海森堡自旋的统一研究

A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

使用群论方法，我们表明，三角形和正方形晶格，在连续极限的反铁磁序参量生活在SO 3不尊重初始晶格。对于反铁磁链，我们恢复了Haldron分解。这个序参量与局部规范场相互作用，而不是像文献中隐含的那样与全局规范场相互作用，在我们的方法中，这种相互作用以一种相当自然的方式出现。事实上，这仅仅对应于自旋群通过局域规范场的一种新的扩展。这种基于实除代数的分析适用于低维格。