# Grassmann fields for spanning hyperforests

Centre of Excellence for Mathematics and Statistics of Complex Systems Seminar

#### by Andrea Bedini

Institution: MASCOS/Department of Mathematics and Statistics, The University of Melbourne
Date: Mon 16th August 2010
Time: 3:15 PM
Location: Theatre 1, Alan Gilbert Building, The University of Melbourne

Abstract: The spanning-hyperforest model is a percolative model with the additional constraint of having no cycles where a weight is given to each connected component (tree). Its generating function can be expressed in terms of anti-commuting Grassmann fields, a representation which effectively generalizes Kirchhoff's matrix-tree theorem. Although the spanning-hyperforest model is naturally connected to the Potts model (in the $q \to 0$ limit), this novel representation uncover a new connection with super-symmetric vector models. Under the light of this "magnetic"
interpretation we study the model on the complete graph, we identify a "low-temperature" phase characterized by the appearance of a giant connected component and delimited by a second order phase transition associated with the super-symmetry breaking.

Drinks and nibbles will be provided afterwards at 139 Barry St.