Actes des rencontres du CIRM

This is an abstract of a work in progress. The first part – Ising model fog drip: the first two droplets – is published in “In and Out of Equilibrium 2”, Progress in Probability, Birkhauser, 2008.

We study the model of the stalagmite formation. It is a result of the dew-fall effect, when the concentration of the vapor exceeds the saturation point. It turns out that the growth process has discontinuities, when a new atomic monolayer is created spontaneously. An interesting feature of the process is that the size of each newly born monolayer has to exceed some critical size $C_cr N$, where $N$ is the linear size of our 3D system. The study boils down to the investigation of the ensemble of the nested random loops in 2D, which are under the influence of two competing mechanisms: entropic repulsion and weak attraction.