Quasi Long Range ordered Phase in 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 {\it frozen-in} power law spin-spin correlation. Numerical estimate of the power-law exponent $\eta = 0.5(2)$ is consistent with the field theoretical analysis, but a possibility of non-universal behavior cannot be excluded.