Quasi-long-range order in random-anisotropy Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) with random uniaxial single-site anisotropy on L×L×L simple cubic lattices, for L up to 64. The spin variable on each site is chosen from the 12 [110] directions. The random anisotropy has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. In many respects the behavior of this model is qualitatively similar to that of the corresponding random-field model. Due to the discretization, for small x at low temperature there is a [110] FM phase. For $x>0$ there is an intermediate quasi-long-range-ordered (QLRO) phase between the paramagnet and the ferromagnet, which is characterized by a |k|^-3 divergence of the magnetic structure factor S(k) for small k, but no true FM order. At the transition between the paramagnetic and QLRO phases S(k) diverges like |k|^-2. The limit of stability of the QLRO phase is somewhat greater than $x=0.5.$ For x close to 1 the low-temperature form of S(k) can be fit by a Lorentzian, with a correlation length estimated to be 11±1 at $x=1.0$ and 25±5 at $x=0.75.$