9 N ov 2 00 4 Potts Model On Random Trees

N ov 2 00 1 Scaling Exponent for Coarsening in a 1 D q - state system

An exponent β which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length 〈l〉. β is defined by P ∼ 〈l〉β−1. We propose a new model of coarsening that prevents correlations from developing b...

ar X iv : m at h - ph / 0 50 70 67 v 3 2 8 N ov 2 00 5 Improved mixing bounds for the Anti - Ferromagnetic Potts Model on Z 2 ∗

We consider the anti-ferromagnetic Potts model on the the integer lattice Z. The model has two parameters, q, the number of spins, and λ = exp(−β), where β is “inverse temperature”. It is known that the model has strong spatial mixing if q > 7, or if q = 7 and λ = 0 or λ > 1/8, or if q = 6 and λ = 0 or λ > 1/4. The λ = 0 case corresponds to the model in which configurations are proper q-colouri...

1 7 N ov 2 00 4 Cosine Products , Fourier Transforms , and Random Sums ∗

ar X iv : h ep - t h / 05 11 16 1 v 2 1 9 N ov 2 00 6 The Effective Potential in the Massive φ 4 4 Model

ar X iv : h ep - l at / 9 70 40 20 v 1 3 0 A pr 1 99 7 Potts Models on Feynman Diagrams

We investigate numerically and analytically Potts models on " thin " random graphs – generic Feynman diagrams, using the idea that such models may be expressed as the N → 1 limit of a matrix model. The thin random graphs in this limit are locally tree-like, in distinction to the " fat " random graphs that appear in the planar Feynman diagram limit, N → ∞, more familiar from discretized models o...