Random anisotropy models in the Ising limit

We have performed Monte Carlo simulations on the random anisotropy axis model of Harris, Plischke, and Zuckermann (introduced to describe amorphous magnetic films such as Dy-Cu or Dy-Al) in the Ising-like limit of infinite anisotropy energy. The ground state of this model (studied in samples of up to 20 × 20 × 20 spins) exhibits significant short-range ferromagnetic order but no long-range magnetic order in three dimensions, supporting arguments of Pelcovits, Pytte, and Rudnick. The specific heat shows a narrow maximum but no obvious critical behavior. Relaxation studies provide evidence for a distinct stable low-temperature phase, but cannot determine whether a sharp phase transition occurs. The spin susceptibility at higher temperatures and magnetization as a function of field at low temperatures have been calculated. Although the absence of critical behavior in the specific heat of this model in zero field is reminiscent of some Ising spin-glasses, the magnetic behavior is indistinguishable from that of a ferromagnet with moderate coercivity.