562 research outputs found
General duality for abelian-group-valued statistical-mechanics models
We introduce a general class of statistical-mechanics models, taking values
in an abelian group, which includes examples of both spin and gauge models,
both ordered and disordered. The model is described by a set of ``variables''
and a set of ``interactions''. A Gibbs factor is associated to each variable
and to each interaction. We introduce a duality transformation for systems in
this class. The duality exchanges the abelian group with its dual, the Gibbs
factors with their Fourier transforms, and the interactions with the variables.
High (low) couplings in the interaction terms are mapped into low (high)
couplings in the one-body terms. The idea is that our class of systems extends
the one for which the classical procedure 'a la Kramers and Wannier holds, up
to include randomness into the pattern of interaction. We introduce and study
some physical examples: a random Gaussian Model, a random Potts-like model, and
a random variant of discrete scalar QED. We shortly describe the consequence of
duality for each example.Comment: 26 pages, 2 Postscript figure
Packing Steiner Trees
Let be a distinguished subset of vertices in a graph . A
-\emph{Steiner tree} is a subgraph of that is a tree and that spans .
Kriesell conjectured that contains pairwise edge-disjoint -Steiner
trees provided that every edge-cut of that separates has size .
When a -Steiner tree is a spanning tree and the conjecture is a
consequence of a classic theorem due to Nash-Williams and Tutte. Lau proved
that Kriesell's conjecture holds when is replaced by , and recently
West and Wu have lowered this value to . Our main result makes a further
improvement to .Comment: 38 pages, 4 figure
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