39,741 research outputs found
Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
We consider the Edwards-Anderson Ising spin glass model on the half-plane with zero external field and a wide range of choices, including
mean zero Gaussian, for the common distribution of the collection J of i.i.d.
nearest neighbor couplings. The infinite-volume joint distribution
of couplings J and ground state pairs with periodic
(respectively, free) boundary conditions in the horizontal (respectively,
vertical) coordinate is shown to exist without need for subsequence limits. Our
main result is that for almost every J, the conditional distribution
is supported on a single ground state pair.Comment: 20 pages, 3 figure
The Real Meaning of Complex Minkowski-Space World-Lines
In connection with the study of shear-free null geodesics in Minkowski space,
we investigate the real geometric effects in real Minkowski space that are
induced by and associated with complex world-lines in complex Minkowski space.
It was already known, in a formal manner, that complex analytic curves in
complex Minkowski space induce shear-free null geodesic congruences. Here we
look at the direct geometric connections of the complex line and the real
structures. Among other items, we show, in particular, how a complex world-line
projects into the real Minkowski space in the form of a real shear-free null
geodesic congruence.Comment: 16 page
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
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
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