Theoretical modeling of prion disease incubation.

We apply a theoretical aggregation model to laboratory and epidemiological prion disease incubation time data. In our model, slow growth of misfolded protein aggregates from small initial seeds controls the latent or lag phase; aggregate fissioning and subsequent spreading leads to an exponential growth phase. Our model accounts for the striking reproducibility of incubation times for high dose inoculation of lab animals.

Reversal-field memory in the hysteresis of spin glasses.

We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a nonanalyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use first order reversal curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films.

Using hysteresis for optimization.

We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is endowed with a suitable "distance." We test the new algorithm on frustrated magnetic models and the traveling salesman problem.

Statistical mechanics of prion diseases.

We present a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., mad cow disease) with concomitant prion protein misfolding and aggregation.

Disorder averaging and finite-size scaling.

We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model.