Seminar

Stochastic geometric methods are known to be a very useful tool for solving a variety of problems in statistical mechanics. Furthermore, problems arising due to this approach are interesting in their own right.

First, familiar Fortuin-Kasteleyn (FK) representation for Classical Ising model is presented via the language of Poisson Point Processes.
In this way, the usual FK representation emerges as an instance of Lie-Trotter product formula.

Next, FK representation is generalized to quantum Ising models in transverse field. This method was originally developed by M.
Campanino, A. Klein, J.F. Perez (1991) and M. Aizenman, A. Klein, C.M.
Newman (1993).

We apply the above Stochastic Geometric reprsentation to the Quantum Curie-Weiss model in transversal field (the Quantum Ising model on complete graph) in order to derive results on the phase diagram of the model.