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

8-10 April 2019
Villa Finaly
Europe/Rome timezone

## Wetting, disordered pinning and layering for discrete random interfaces

8 Apr 2019, 14:10
50m
Villa Finaly

#### Villa Finaly

Via Bolognese, 134 R 50139 Florence Italy

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 $\phi$, $\mathbb Z^{d-1} \to \mathbb Z$. 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: $$V(\phi)=\beta \sum_{x\sim y}|\phi(x)-\phi(y)|-\sum_{x}\left( h\ind_{\{\phi(x)=0\}}-\infty\ind_{\{\phi(x)=0\}} \right).$$ 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.