434 research outputs found
Potts models on hierarchical lattices and Renormalization Group dynamics
We prove that the generator of the renormalization group of Potts models on
hierarchical lattices can be represented by a rational map acting on a
finite-dimensional product of complex projective spaces. In this framework we
can also consider models with an applied external magnetic field and
multiple-spin interactions. We use recent results regarding iteration of
rational maps in several complex variables to show that, for some class of
hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of
the renormalization map.Comment: 21 pages, 7 figures; v3 revised, some issues correcte
Mini-Workshop: Hypergraph Turan Problem
This mini-workshop focused on the hypergraph Turán problem. The interest in this difficult and old area was recently re-invigorated by many important developments such as the hypergraph regularity lemmas, flag algebras, and stability. The purpose of this meeting was to bring together experts in this field as well as promising young mathematicians to share expertise and initiate new collaborative projects
Grassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J.
Phys.
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