阻挫$S^{2}$值自旋系统的手征跃迁

阻挫铁磁自旋链：手征跃迁的变分方法

Frustrated ferromagnetic spin chains: a variational approach to chirality transitions

我们研究了一维铁磁/反铁磁受抑自旋链的能量，其中最近和次最近的相互作用接近helimagnet/铁磁转变点的粒子数发散。我们严格证明了手性基态的出现，我们计算，通过执行适当的重整化和缩放的伽玛极限，为手性过渡的能量。

Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions

We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$ spin model on the square lattice in the vicinity of the helimagnet/ferromagnet transition point as the lattice spacing vanishes. Carrying out the $Γ$-convergence analysis of proper scalings of the energy, we prove the emergence and characterize the geometric rigidity of the chirality phase transitions.

一维和二维受挫自旋系统的变分分析：手性相变与磁各向异性相变

Variational analysis in one and two dimensions of a frustrated spin system: chirality transitions and magnetic anisotropic transitions

本文通过$Γ$-极限方法分析一维和二维受挫自旋系统在螺旋磁体/铁磁体相变点附近的能量渐近行为，揭示磁各向异性转变与手性转变的能量代价及二维手性转变的几何刚性。

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.

Variational analysis of the $J_1$-$J_2$-$J_3$ model: a non-linear lattice version of the Aviles-Giga functional

We study the variational limit of the frustrated $J_1$-$J_2$-$J_3$ spin model on the square lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. We carry out the $Γ$-convergence analysis of proper scalings of the energy and we characterize the optimal cost of a chirality transition in $BV$ proving that the system is asymptotically driven by a discrete version of a non-linear perturbation of the Aviles-Giga energy functional.

Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble

We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian orthogonal ensemble (Cartan class B$|$DI) and the ensemble of antisymmetric Hermitian random matrices (Cartan class B$|$D). It enjoys the special feature that, depending on the matrix dimension $N$, it has exactly $ν=0$ $(1)$ zero-mode for $N$ even (odd), throughout the symmetry transition. This "topological protection" is reminiscent of properties of topological insulators. We show that our ensemble represents a Pfaffi…