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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
Comment on "Nonlinear current-voltage curves of gold quantum point contacts" [Appl. Phys. Lett. 87, 103104 (2005)]
In a recent Letter [Appl. Phys. Lett. 87, 103104 (2005)], Yoshida et al.
report that nonlinearities in current-voltage curves of gold quantum point
contacts occur as a result of a shortening of the distance between electrodes
at finite bias, presumably due to thermal expansion. For short wires, the
electrode displacement induces a thickening of the wire, as well as
nonlinearities of the IV curve, while the radius of long wires is left
unchanged, thus resulting in a linear IV curve. We argue here that electron
shell effects, which favor wires with certain "magic radii," prevent the
thickening of long wires under compression, but have little effect on wires
below a critical length.Comment: Version accepted for publication in Applied Physics Letter
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