Abstract
The Kagome lattice is THE prototype lattice to study effects of geometric frustration. Both classical and quantum models on this and related lattices are still under heavy debate. For the quantum model even the ground state is not clear. As for this lattice there is no work-around to avoid the fermion sign problem (e.g. projective QMC does not work), the dynamics is largely inaccessible. This makes the study of the classical limit, and therefore the classical model interesting.
In this talk I will review some known facts about the classical Kagome lattice Heisenberg model and then present some of our recent work on this model:
It is known that this model is highly degenerate and does not possess ordering at zero temperature. At non-zero temperature certain states are selected via the 'order-by-disorder' mechanism. The low temperature phase can be described by nematic order. More recently the octopular order parameter was proposed as an alternative description. Monte Carlo simulations revealed a peculiar finite-size behavior leaving conclusions for the thermodynamic limit uncertain. Possible AFM correlations or ordering has been debated.
We study this problem numerically with the help of parallel tempering and by introducing an additional term coupling between the next-nearest spins. This lifts some degeneracies and introduces a bias, depending on the sign chosen, towards one of two possible sub-lattice Neel orders. Upon tuning the J2-term for both signs towards the pure Heisenberg model, we observe finite-size scaling consistent with phase transitions for certain universality classes.
Coffee and tea will be served 20 minutes prior to the seminar.