Degeneracy and ordering of the noncoplanar phase of the classical bilinearbiquadratic Heisenberg model on the triangular lattice
Abstract
We investigate the zerotemperature 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 Φ∈(0,2π/3). In this situation, the ground states are noncoplanar and have an infinite discrete degeneracy. In the generic case, i.e., when Φ≠π/2,arccos(1/3), the groundstate manifold is in onetoone correspondence (up to a global rotation) with the set of noncrossing 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 longrange order in terms of spin orientation. This conclusion is further supported by the comparison with the fourstate antiferromagnetic Potts model [describing the Φ=arccos(1/3) case], which at zero temperature is critical and in terms of the solidonsolid representation is located exactly at the point of roughening transition. At Φ≠arccos(1/3), an additional constraint appears, whose presence drives the system into an ordered phase (unless Φ=π/2, when another constraint is removed and the model becomes trivially exactly solvable).
 Publication:

Physical Review B
 Pub Date:
 May 2012
 DOI:
 10.1103/PhysRevB.85.174420
 arXiv:
 arXiv:1202.3214
 Bibcode:
 2012PhRvB..85q4420K
 Keywords:

 75.10.Hk;
 75.50.Ee;
 05.50.+q;
 Classical spin models;
 Antiferromagnetics;
 Lattice theory and statistics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 10 pages, 5 figures