Young, Peter
Title: Monte Carlo Simulations of Heisenberg Spin Glasses
Author: Peter Young
Affiliation: University of California Santa Cruz, USA
Abstract:
Whereas most numerical studies on spin glasses have focussed on the Ising case, since this is the simplest, there are new features associated with vector spin glasses which need to be elucidated. Here I will discuss results of simulations on 3-component (Heisenberg) spin glasses. Equilibration is hard at low temperatures because of the "many-valley" energy landscape, and so, as with the Ising case, the method of "parallel tempering" is used to speed things up. From a computational perspective, there are two surprises. The first is that, although the code to update a spin is much more complicated and hence more time consuming than that for the Ising case, one can actually equilibrate much larger sizes for the Heisenberg spin glass, indicating that the barriers between valleys are smaller for Heisenberg spin glasses. Presumably vector spins can, to some extent, go round barriers rather than over them. The second surprise is that adding "overrelaxation" moves, introduced initially just because they are simpler and hence execute more quickly than "heatbath" moves, equilibrates the system much more efficiently than if one had just heatbath moves. I will also discuss some of the physics results that have emerged from these simulations.
Author: Peter Young
Affiliation: University of California Santa Cruz, USA
Abstract:
Whereas most numerical studies on spin glasses have focussed on the Ising case, since this is the simplest, there are new features associated with vector spin glasses which need to be elucidated. Here I will discuss results of simulations on 3-component (Heisenberg) spin glasses. Equilibration is hard at low temperatures because of the "many-valley" energy landscape, and so, as with the Ising case, the method of "parallel tempering" is used to speed things up. From a computational perspective, there are two surprises. The first is that, although the code to update a spin is much more complicated and hence more time consuming than that for the Ising case, one can actually equilibrate much larger sizes for the Heisenberg spin glass, indicating that the barriers between valleys are smaller for Heisenberg spin glasses. Presumably vector spins can, to some extent, go round barriers rather than over them. The second surprise is that adding "overrelaxation" moves, introduced initially just because they are simpler and hence execute more quickly than "heatbath" moves, equilibrates the system much more efficiently than if one had just heatbath moves. I will also discuss some of the physics results that have emerged from these simulations.