Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

Extensive Monte Carlo simulations are used to investigate the low-temperature properties of the random anisotropy Heisenberg model, which describes the magnetic behavior of amorphous rare-earth-transition metal alloy. We show that the low-temperature phase in weak-anisotropy region is characterized by a frozen-in power-law spin-spin correlation. Numerical observation of the power-law exponent $\eta$ indicates nonuniversal behavior.