The XY Antiferromagnet on Some Plane Triangulations

Details The XY Antiferromagnet on Some Plane Triangulations The XY Antiferromagnet on Some Plane Triangulations

2012-01-20

arxiv.org/abs/1201.4309v1

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, 6 figures

Scientific paper

Using Monte Carlo simulation and finite-size scaling, we investigate the $XY$ antiferromagnet on the triangular, union-jack (UJ) and bisected hexagonal (BH) lattices, and find an Ising-type as well as a Kosterlitz-Thouless(KT)-type transition. On the triangular lattice, as temperature decreases, the system develops a nonzero chiral order for $J > J_{\rm Ising} $ and then a quasi-long-range magnetic order for spins on sublattices for $J > J_{\rm KT} > J_{\rm Ising}$, with $J$ the coupling strength. On the UJ and BH lattices, in contrast, as temperature increases the chiral order is destroyed first at $J_{\rm Ising}$ while the spins on some or all the sublattices remain to be quasi-long-range ordered until $J_{\rm KT}$ $(< J_{\rm Ising})$. Further, different magnetic properties for the $XY$ antiferromagnet on these plane triangulations are observed near $J_{\rm Ising}$, near $J_{\rm KT}$, as well as in the intermediate region in between.

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