Sacha Friedli

Non-analyticity and the van der Waals limit

We study the analyticity properties of the free energy fγ(m) of the Kac model at points of first order phase transition, in the van der Waals limit γ↘0. We show that there exists an inverse temperature β0 and γ0>0 such that for all β≥β0 and for all γ∈(0,γ0), fγ(m) has no analytic continuation along the path m↘m* (m* denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure pγ(h), which is related to the free energy fγ(m) by a Legendre transform.

Scaling Limit of the Prudent Walk

We describe the scaling limit of the nearest neighbour prudent walk on

On the Truncation of Systems with Non-Summable Interactions

Z^2

Rigorous analysis of singularities and absence of analytic continuation at first-order phase-transition points in lattice-spin models.

, which performs steps uniformly in directions in which it does not see sites already visited. We show that the scaling limit is given by the process

Statistical mechanics of lattice systems : a concrete mathematical introduction

Z_u = \int_0^{3u/7} ( \sigma_1 1_{W(s)\geq 0}\vec{e}_1 + \sigma_2 1_{W(s)\geq 0}\vec{e}_2 ) ds

On the Singularity of the Free Energy at a First Order Phase Transition

,

A note on the Bramson–Kalikow process

u \in [0,1]

On long range percolation with heavy tails.

, where

Subcritical percolation with a line of defects

W

The Ising Model

is the one-dimensional Brownian motion and