Irreversibility and metastability in spin-glasses. II. Heisenberg model

We numerically compute the various history-dependent magnetizations for Heisenberg spinglasses with and without anisotropy. The exchange interactions are of short range and have a Gaussian probability distribution. Our approach closely follows that of paper I. In the absence of anisotropy, a Heisenberg spin-glass is found to have no irreversibility. The field-cooled and zero-field-cooled magnetizations are macroscopically equivalent and magnetic hysteresis is absent. This macroscopic reversibility is a consequence of the accessibility of the rotationally degenerate field-cooled state and does not correspond to microscopic reversibility. Both Dzyaloshinsky-Moriya (DM) and uniaxial anisotropy introduce macroscopic irreversibility. In the latter case the hysteresis loops are like those which we found for Ising spins. In the former case, in some situations, we find displaced loops, which look similar to those seen in Mn-containing spin-glasses. To get qualitative agreement with experiment, we must also impose a tendency towards ferromagnetism. This ferromagnetic tendency (which corresponds to a displaced Gaussian exchange distribution with $J_0>0\mathrm{}$) is essential in order to maintain rigid rotation of the spins in response to field rotations. This rigidity is a fundamental assumption in other approaches which explain analytically why DM anisotropy leads to displaced hysteresis loops. Finally we study the coexistent (longitudinal) ferromagnetic—(transverse) spin-glass phase proposed by Gabay and Toulouse. The behavior of the coexistent spin-glass is very similar to that of typical spin-glasses in very large applied fields. We see no indication for reentrant behavior, as is often observed experimentally, in our temperature-dependent moderate-field magnetizations. Furthermore, a calculation of the zero-field ($J_0,T$) phase diagram for isotropic systems shows no evidence for reentrant behavior. We cannot rule out the possibility that a reentrant transition exists only in some narrow range of low magnetic fields.