Equilibrium and Non-equilibrium Statistical Mechanics A conference in honor of François Dunlop

Wetting, disordered pinning and layering for discrete random interfaces

8 avr. 2019, 14:10

50m

Villa Finaly

Orateur

Hubert Lacoin

Description

Solid-on-Solid (SOS) is a simplified surface model which has been introduced to understand the behavior of Ising interfaces in ${\mathbb{Z}}^d$ at low temperature. The simplification is obtained by considering that the interface is a graph of a function $\varphi$, ${\mathbb{Z}}^{d-1}\to \mathbb{Z}$. In the present talk, we study the behavior of SOS surfaces in ${\mathbb{Z}}^2$ constrained to remain positive, and interacting with a potential when touching zero, corresponding to the energy functional: $$\text{Undefined control sequence ind}$$ We show that if $\beta$ is small enough, the system undergoes a transition from a localized phase where there is a positive fraction of contact with the wall to a delicalized one for $$h_w(\beta )=\log \left(\frac{e^{4\beta }}{e^{4\beta }-1}\right).$$ In addition by studing the free energy, we prove that the system undergoes countably many layering transitions, where the typical height of the interface jumps between consecutive integer values. We also discuss the case of the disordered model without positivity constraint.

Documents de présentation

Florence2019_Lacoin.pdf