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

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

2012-02-15

arxiv.org/abs/1202.3214v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 5 figures

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-556552