Tunca, EgemenBerker, A. Nihat2023-10-192023-10-19202322470-00452470-0053https://doi.org/10.1103/PhysRevE.107.014116https://hdl.handle.net/20.500.12469/5077Nematic 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.eninfo:eu-repo/semantics/openAccessHierarchical LatticesSymmetry-BreakingRenormalizationModelsParameterHierarchical LatticesSymmetry-BreakingRenormalizationModelsParameterArticle1107WOS:00092126260000610.1103/PhysRevE.107.0141162-s2.0-85146644005Q1Q136797935