Transverse Ising Spin Glass and Random Field Systems

Abstract

AbstractSpin glasses are magnetic systems with randomly competing (frustrated) interactions [6.1]. Here, the frustration arises due to the competing (ferromagnetic and antiferromagnetic) quenched random interactions between the spins. The spins in such systems get frozen in random orientations below a certain transition temperature. Although there is no long range magnetic order, i.e., the space averages of the spin moments vanish, the spins are frozen over macroscopic scales of time and hence the time average of any spin is nonzero below the (spin glass) transition temperature. This time average is treated as a measure of the spin freezing or spin glass order parameter. Because of frustration, the ground state is (infinitely) degenerate; the degeneracy being of the order of exp(N) for a system of N spins. These ground states, as well as the local minima, are however, often separated by macroscopically large energy barriers (O(N)) which force the system to get trapped, depending on its history (initial configuration), in one of its degenerate (local) minima. The system thus becomes “nonergodic” and a spin glass may be described by a nontrivial order parameter distribution [6.2] in the thermodynamic limit (unlike the unfrustrated cooperative systems, where the distribution becomes trivially delta function-like in the same limit).KeywordsSpin GlassQuantum FluctuationTransverse FieldTricritical PointSpin Glass ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.