On the dynamics of Heisenberg magnets with lattice anisotropy near the phase transition

Walter Selke

Ha M. Nguyen, Pai‐Yi Hsiao

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 Kc=0.704 35(2) and Kc=0.709 98(4), respectively. While the critical exponent 1/ν=1.408 24(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.

N. S. Branco, Anna Chame

Shin-ichiro Yoshikawa, Kouichi Okunishi, Makoto Senda +1 more

The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S=1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also found that the similarity of the selected states in the classical and quantum models are not the case in a two-leg ladder lattice, although the lattice consists of triangles locally and the ground state of this lattice in the classical case is the same as that of the triangular lattice.

Alex Bunker, Kun Chen, David Paul Landau

Jürg Martin Fröhlich, Élliott H. Lieb

The two-dimensional anisotropic, nearest-neighbor Heisenberg model on a square lattice, both quantum and classical, has been shown regorously to have a phase transition in the sense that the spontaneous magnetization is positive at low temperatures. This is so for all anisotropies. An analogous result (staggered polarization) holds for the antiferromagnet in the classical case; in the quantum case it holds if the anisotropy is large enough (depending on the single-site spin).