Nematic ordering in the Heisenberg spin-glass system in three dimensions

Axial, planar-diagonal, body-diagonal fields on the cubic-spin spin glass in d=3: A plethora of ordered phases under finite fields

A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high-temperature disordered phase, for number of spin components n≥3, in spatial dimension d=3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), qualitatively different from the conventional spin-glass phase diagram topology, are seen. The chaotic rescaling behaviors and their Lyapunov exponents are calculated in each of these spin-glass phase diagram topologies. These results are obtained from renormalization-group calculations that are exact on the d=3 hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. Axial, planar-diagonal, or body-diagonal finite-strength uniform fields are applied to n=2 and 3 component cubic-spin spin-glass systems in d=3.

Reentrant ferromagnetic ordering of the random-field Heisenberg model in d>2 dimensions: Fourier-Legendre renormalization-group theory

The random-magnetic-field classical Heisenberg model is solved in spatial dimensions d≥2 using the recently developed Fourier-Legendre renormalization-group theory for 4π steradians continuously orientable spins, with renormalization-group flows of 12 500 variables. The random-magnetic-field Heisenberg model is exactly solved in 10 hierarchical models, for d=2,2.26,2.46,2.58,2.63,2.77,2.89,3. For nonzero random fields, ferromagnetic order is seen for d>2. This ordering, at d=2.46,2.58,2.63,2.77,2.89,3, shows reentrance as a function of temperature.