TEBIP High Performers Program, Board of Higher Education of Turkey, Istanbul University, Fatih, Istanbul 34452, Turkey.
Faculty of Engineering and Natural Sciences, Kadir Has University, Cibali, Istanbul 34083, Turkey.
Phys Rev E. 2023 Jan;107(1-1):014116. doi: 10.1103/PhysRevE.107.014116.
Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in d=3. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. This nematic ordering of the Heisenberg spin-glass system is dramatically different from the spin-glass ordering of the Ising spin-glass system. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions d>2: We calculate nematic transition temperatures in 24 different dimensions in 2<d≤4.
向列有序，其中自旋整体沿一个自发选择的轴对齐，而与方向无关，发生在经典海森堡自旋的自旋玻璃系统中，d=3。在这个系统中，最近邻相互作用随机淬火为铁磁或反铁磁，而不是局部随机有序的自旋玻璃相，系统整体有序为向列相。这种海森堡自旋玻璃系统的向列有序与伊辛自旋玻璃系统的自旋玻璃有序显著不同。该系统在分层晶格上被精确求解，等效地，在立方晶格上被 Migdal-Kadanoff 近似求解。计算了全局相图，展示了向列相、铁磁相、反铁磁相和无序相。在其他维度 d>2 中也发现了经典海森堡自旋玻璃系统的向列相：我们在 2<d≤4 的 24 个不同维度中计算了向列相变温度。
