Theoretical Studies of Frustrated Systems

University Of California-Santa Cruz, Santa Cruz CA

Investigators

Abstract

This grant supports theoretical and computational research on systems with frustration, i.e., competition, in their interactions. The work will focus on a particular set of systems that is convenient to study, the spin glass. However, the results of this research will have wide applicability. The dynamics of spin glasses at low temperatures is very slow because the system gets trapped in local minima. A range of surprising non-equilibrium effects have been observed experimentally, but these have been hard to see in simulations on Ising systems, i.e., systems with discrete spins. In previous work the need to investigate vector spin glass systems has been emphasized, and indeed the non-equilibrium effects are seen more strongly in experiments on vector spin glasses than Ising spin glasses. Thus, non-equilibrium and equilibrium behavior of vector spin glasses will be studied with the intent of explaining experimental results in detail. Also, studies will be made to find algorithms that are more efficient than those currently available. For finite-temperature simulations, the best current techniques for speeding up equilibration is parallel tempering, in which the temperature of the system wanders up and down, so it can easily overcome barriers when at high temperature. We will investigate if using quantum, rather than thermal, fluctuations will be more efficient. Already there is evidence that the quantum analogue of "simulated annealing," which is used to find the ground states but does not give equilibrium behavior at finite temperature, is more efficient than the original thermal version. We will also investigate a quite different algorithm, based on a calculation of the density of states, from which one can, in principle, get information about any temperature. On a longer time frame, we will investigate whether an algorithm used with great success for a problem in combinatorial optimization, but rooted in ideas from spin glasses, can be used to find spin glass ground states more efficiently. Since numerical studies of spin glasses are inevitably restricted to rather small sizes, even with the best available algorithms, it is useful to find models which approach the asymptotic critical behavior as fast as possible on increasing the size. Thus, we will study a family of spin glass models to try to find a subspace in which the leading correction to finite-size scaling vanishes, which would enable reliable results to be obtained from smaller lattice sizes. The results of these studies on spin glasses will have wide applicability to other fields of study. In addition, this research provides excellent training for students. %%% This grant supports theoretical and computational research on systems with frustration, i.e., competition, in their interactions. The work will focus on a particular set of systems that is convenient to study, the spin glass. The results of these studies on spin glasses will have wide applicability to other fields of study. In addition, this research provides excellent training for students. ***