Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices
in a strong external magnetic field are mapped onto hard-core lattice gases
with an extended exclusion region. The effective models are studied by the
exchange Monte Carlo simulations and by the transfer matrix method. The
transition point and the critical exponents are obtained numerically for a
square-lattice gas of particles with the second-neighbor exclusion, which
describes a checkerboard antiferromagnet. The exact structure of the magnon
crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio
