In cluster tomography, we propose measuring the number of clusters N intersected by a line
segment of length ℓ across a finite sample. As expected, the leading order of N (ℓ) scales as …

Recent cellular-level volumetric brain reconstructions have revealed high levels of anatomic
complexity. Determining which structural aspects of the brain to focus on, especially when …

In this work, some classical results of the pfaffian theory of the dimer model based on the
work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we …

We use scale invariant scattering theory to exactly determine the renormalization group fixed
points of a q-state Potts model coupled to an r-state Potts model in two dimensions. For …

We consider the partition functions of the anisotropic dimer model on the rectangular (2 M−
1)×(2 N− 1) lattice with (a) free and (b) cylindrical boundary conditions with a single …

In this work we obtain wrapping probabilities for Ising spin clusters on a torus. We use the
analogy with the tricritical point of a Potts model with dilution. The formula obtained are …

In three-dimensional critical percolation we study numerically the number of clusters N Γ
which intersect a given subset of bonds Γ. If Γ represents the interface between a subsystem …

Determining whether an additional local symmetry affects the universality class of a sta-
tistical model is an important issue in the theory of critical phenomena. A basic example is …

We consider the random-bond Potts model in the large-Q limit and calculate the excess
entropy, S Γ, of a contour, Γ, which is given by the mean number of Fortuin–Kasteleyn …

Tout d'abord, je tiens à remercier Malte pour avoir accepté d'être mon directeur de thèse et
de m'avoir tant appris durant ces trois années. Cette thèse témoigne de sa double …