The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.

arXiv:1101.2127Physical Review EApr 15, 201119 citations

Magnetic and nematic orderings in spin-1 antiferromagnets with single-ion anisotropy

Keola Wierschem, Yasuyuki Kato, Yusuke Nishida +2 more

We study a spin-1 Heisenberg model with exchange interaction $J$ , uniaxial single-ion exchange anisotropy $D$ , and Zeeman coupling to a magnetic field $B$ parallel to the symmetry axis. We compute the $(D/J,B/J)$ quantum phase diagram for square and simple cubic lattices by combining analytical and quantum Monte Carlo approaches, and find a transition between $XY$ antiferromagnetic and ferronematic phases that spontaneously break the $U(1)$ symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new avenues for measuring this transition in real magnets.We study a spin-1 Heisenberg model with exchange interaction $J$, uniaxial single-ion exchange anisotropy $D$, and Zeeman coupling to a magnetic field $B$ parallel to the symmetry axis. We compute the $(D/J,B/J)$ quantum phase diagram for square and simple cubic lattices by combining analytical and quantum Monte Carlo approaches, and find a transition between $XY$ antiferromagnetic and ferronematic phases that spontaneously break the $U(1)$ symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new avenues for measuring this transition in real magnets.

arXiv:1209.0688Physical Review BNov 30, 201222 citations

Two-dimensional Heisenberg model with weak anisotropy

S.B. Khokhlachev

Journal of Experimental and Theoretical PhysicsJan 1, 19763 citations

A Quantum Monte Carlo Method for the Heisenberg Spin System

J. W. Lyklema

Springer eBooksJan 1, 19841 citation

We study a spin-1 Heisenberg model with exchange interaction

J

, uniaxial single-ion exchange anisotropy

D

, and Zeeman coupling to a magnetic field

B

parallel to the symmetry axis. We compute the

(D/J,B/J)

quantum phase diagram for square and simple cubic lattices by combining analytical and quantum Monte Carlo approaches, and find a transition between

XY

antiferromagnetic and ferronematic phases that spontaneously break the

U(1)

symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new avenues for measuring this transition in real magnets.