2,015 research outputs found
Critical temperature of Heisenberg models on regular trees, via random loops
We estimate the critical temperature of a family of quantum spin systems on
regular trees of large degree. The systems include the spin- XXZ model
and the spin-1 nematic model. Our formula is conjectured to be valid for
large-dimensional cubic lattices. Our method of proof uses a probabilistic
representation in terms of random loops.Comment: 14 pages, to appear in J. Stat. Phy
Large random simplicial complexes, I
In this paper we introduce a new model of random simplicial complexes
depending on multiple probability parameters. This model includes the
well-known Linial - Meshulam random simplicial complexes and random clique
complexes as special cases. Topological and geometric properties of a
multi-parameter random simplicial complex depend on the whole combination of
the probability parameters and the thresholds for topological properties are
convex sets rather than numbers (as in all previously known models). We discuss
the containment properties, density domains and dimension of the random
simplicial complexes.Comment: 21 pages, 6 figure
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