Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?

We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on the infinite square lattice are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show --- much less likely in our opinion --- that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.Comment: 18 pages (LaTeX); 1 figure; minor revisions; to appear in Commun. Math. Phy

Asian Crises: Theory, Evidence, Warning-Signals

In July 1997, the economies of East Asia became embroiled in one of the worst financial crises of the postwar period. Yet, prior to the crisis, these economies were seen as models of economic growth experiencing sustained growth rates that exceeded those earlier thought unattainable. Why did the market not anticipate the crises? To this end, we review the Asian financial crisis from two related perspectives - whether the crisis was precipitated by a failure of the real exchange rate to be aligned with its fundamental determinants and/or whether the crisis was precipitated by a divergence of the foreign debt from its optimal path. The first perspective is based on a coherent theory of the equilibrium real exchange rate - the NATREX model - that shows how “misalignments” lead to currency crises. The second perspective is based on a model of optimal foreign debt ratio - derived from stochastic optimal control - which shows why “divergences” lead to debt crises. The important point here is that these models suggest important variables which may serve as warning signals to predict crises.Asian crises, optimal debt, equilibrium exchange rates, NATREX, stochastic optimal control, warning signals of crises, exchange rate misalignment