Orateur
Description
In this talk we will make a survey of how techniques of ``Grassmann
Calculus'', that is, integration of expressions involving
anticommuting variables, provide fermionic analogues of Gaussian
integration, Wick's Theorem and perturbative field theory. These
techniques are specially fruitful for describing certain combinatorial
models in Statistical Mechanics, namely $n=2$ Loop Models, Spanning
Trees, and Spanning Forests.
If the time permits, we will also show how the model of Spanning
Forests, in its Grassmann-variable formulation, has a hidden
$\mathrm{OSp}(1|2)$ supersymmetry, that, by the Parisi--Sourlas
mechanism, implies that it must be in the same universality class of
the $O(n)$ loop model in the analytic continuation $n\to -1$.
Mostly based on (old) works in collaboration with S. Caracciolo and
A.D. Sokal.
