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Magnetic phase transition (MPT) to magnetic quasi-long-range order (QLRO)phase in a three-dimensional Heisenberg weak (D/J=4) random anisotropy (RA)model is investigated by Monte Carlo simulation. The isotropic and cubicdistributions of RA axes are considered for simple-cubic-lattice systems.Finite-size scaling analysis shows that the critical couplings for the formerand latter are K_c= 0.70435(2) and K_c=0.70998(4), respectively. While thecritical exponent 1/\nu =1.40824(0) is the same for both cases. A second-orderMPT to the QLRO phase is therefore evidenced to be possible in favor with theexistence of the QLRO predicted by recent functional renormalization grouptheories.

Mangetic phase transition for three-dimensional Heisenberg weak random anisotropy model: Monte Carlo study