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Abstract:

This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and illustrate the richness that has arisen, in conceptual understanding, in methodology and in application, across a large range of scientific disciplines, together with a hint of some of the further opportunities that remain to be tapped. In doing so, it takes the perspective of physics and tries to show, albeit rather briefly, how physics has contributed and been stimulated.

Abstract:

For systems that self-assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems can lead to significant finite-size effects due to the suppression of concentration fluctuations. We introduce methods for estimating the bulk yields from simulations of small systems and for following the convergence of yields with system size, under the assumptions that the various species behave ideally. © 2010 IOP Publishing Ltd.

Abstract:

We study charged excitations of the non-Abelian Moore-Read liquid at a filling factor ν=52, allowing for spin depolarization. Using a combination of numerical studies, and taking account of nonzero well widths, we find that at a sufficiently low Zeeman energy it is energetically favorable for charge e/4 quasiholes to bind into Skyrmions of charge e/2. We show that Skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized ν=52 ground state in realistic experimental situations. We comment on the consequences for the activated transport. © 2010 The American Physical Society.