Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings

Details Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings

2010-04-26

arxiv.org/abs/1004.4627v2

Phys. Rev. E 82, 031113 (2010)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 8 figures

Scientific paper

10.1103/PhysRevE.82.031113

We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbour interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order-by-disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R^2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin-S Kitaev model for large S, and obtain lower and upper bounds on the ground state energy of the quantum model.

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