1202.3214 (S. E. Korshunov et al.)

Degeneracy and ordering of the non-coplanar phase of the classical
bilinear-biquadratic Heisenberg model on the triangular lattice    [PDF]

S. E. Korshunov, F. Mila, K. Penc

We investigate the zero-temperature behavior of the classical Heisenberg
model on the triangular lattice in which the competition between exchange
interactions of different orders favors a relative angle between neighboring
spins in the interval (0,2pi/3). In this situation, the ground states are
noncoplanar and have an infinite discrete degeneracy. In the generic case, the
set of the ground states is in one to one correspondence (up to a global
rotation) with the non-crossing loop coverings of the three equivalent
honeycomb sublattices into which the bonds of the triangular lattice can be
partitioned. This allows one to identify the order parameter space as an
infinite Cayley tree with coordination number 3. Building on the duality
between a similar loop model and the ferromagnetic O(3) model on the honeycomb
lattice, we argue that a typical ground state should have long-range order in
terms of spin orientation. This conclusion is further supported by the
comparison with the four-state antiferromagnetic Potts model [describing the
case when the angle between neighboring spins is equal to arccos(-1/3)], which
at zero temperature is critical and in terms of the solid-on-solid
representation is located exactly at the point of roughening transition. At
other values of the angle between neighboring spins an additional constraint
appears, whose presence drives the system into an ordered phase (unless this
angle is equal to pi/2, when another constraint is removed and the model
becomes trivially exactly solvable).

View original: http://arxiv.org/abs/1202.3214