SP Seminar @SISSA Via Bonomea 265 - Tuesday 19 February 11am - Jesper JACOBSEN

[CM Section]

Joint ICTP/SISSA Statistical Physics Seminar

Tuesday 19 February at 11:00 a.m.
SISSA, Via Bonomea 265, Room 128

Jesper JACOBSEN (ENS, Paris France)

'Four-point Functions in the Fortuin-Kasteleyn
Cluster Model"

Abstract:
The determination of four-point correlation functions of
two-dimensional 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 so-called 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 3-state Potts models.
However, for geometrical observables in the Fortuin-Kasteleyn
cluster formulation of the Q-state 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 warm-up
to solving this problem, we discuss which states propagate
in the s-channel 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.