dc.contributor.author | Cerkauskas, Cyrus | |
dc.date.accessioned | 2019-01-25 21:49:21 (GMT) | |
dc.date.available | 2020-01-26 05:50:12 (GMT) | |
dc.date.issued | 2019-01-25 | |
dc.date.submitted | 2019-01-19 | |
dc.identifier.uri | http://hdl.handle.net/10012/14435 | |
dc.description.abstract | We investigate the bilinear-biquadratic Heisenberg model on the pyrochlore lattice.
While negative biquadratic couplings result in a first-order transition into a nematic ordered
state with spins aligned mutually collinearly, it is found that positive biquadratic
interactions lead to spins orienting in mutually perpendicular directions, described as octupolar
or tetrahedral ordering. This transition is probed using classical Monte Carlo
and it is found that the system undergoes a first-order transition into a octupolar ordered
state with no long-range order. Unfortunately, we find that single spin-flip Monte Carlo
simulations freeze completely at the transition with exceptionally slow dynamics and an
extreme lack of ergodicity. The application of parallel tempering does not improve simulation
results, which, due to the poor ergodicity of the simulation, cannot be reweighted
using histogram techniques. We also present and discuss a potential loop algorithm which
may allow simulations to overcome local energy barriers and regain ergodicity.
Upon warming Monte Carlo simulations initialized in potential octupolar long-range
ordered states, we observe the dynamics of weathervane modes; zero energy rotational excitations
in the lattice. Taking the form of 2D membranes in the lattice, these weathervane
modes may rotate at no energy cost, allowing for the successful use of the single spin-flip
Monte Carlo algorithm. We note that these weathervane modes exist at rotational angles
of 0 and corresponding to alternating layers of spins, in agreement with previous work.
Depending on the long-range ordered state that the simulation is initialized in, weathervane
modes may be stabilized by the periodic boundary conditions or, if free to rotate at
will, may enter a weathervane manifold state where fast dynamics permit the simulation
to rapidly sample various weathervane ordered states. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | monte carlo | en |
dc.subject | biquadratic | en |
dc.subject | octupolar | en |
dc.subject | Heisenberg pyrochlore | en |
dc.subject.lcsh | Heisenberg uncertainty principle | en |
dc.subject.lcsh | Equations, Biquadratic | en |
dc.subject.lcsh | Monte Carlo method | en |
dc.title | Octupolar Ordering in the b>0 Bilinear-Biquadratic Heisenberg Pyrochlore | en |
dc.type | Master Thesis | en |
dc.pending | false | |
uws-etd.degree.department | Physics and Astronomy | en |
uws-etd.degree.discipline | Physics | en |
uws-etd.degree.grantor | University of Waterloo | en |
uws-etd.degree | Master of Science | en |
uws-etd.embargo.terms | 1 year | en |
uws.contributor.advisor | Gingras, Michel | |
uws.contributor.affiliation1 | Faculty of Science | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |