Fourpoint functions in the FortuinKasteleyn cluster model
Seminar/Forum
The determination of fourpoint correlation functions of twodimensional lattice models is of fundamental importance in statistical physics. In the limit of an infinite lattice, this question can be formulated in terms of conformal field theory (CFT). For the socalled minimal models the problem was solved more than 30 years ago, by using that the existence of singular states implies that the correlation functions must satisfy certain differential equations. This settles the issue for models defined in terms of local degrees of freedom, such as the Ising and 3state Potts models. However, for geometrical observables in the FortuinKasteleyn cluster formulation of the Qstate Potts model, for generic values of Q, there is in general no locality and no singular states, and so the question remains open. As a warmup to solving this problem, we discuss which states propagate in the schannel of such correlation functions, when the four points are brought together two by two. To this end we combine CFT methods with algebraic and numerical approaches to the lattice model.
Presenter

Professor Jesper Jacobsen, Ecole Normale Superieure Paris