  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 cubic
distributions of RA axes are considered for simple-cubic-lattice systems.
Finite-size scaling analysis shows that the critical couplings for the former
and latter are K_c= 0.70435(2) and K_c=0.70998(4), respectively. While the
critical exponent 1/\nu =1.40824(0) is the same for both cases. A second-order
MPT to the QLRO phase is therefore evidenced to be possible in favor with the
existence of the QLRO predicted by recent functional renormalization group
theories.
