Related papers: Pinning and wetting transition for (1+1)-dimension…
We consider a random field $\varphi:\{1,...,N\}\to \mathbb{R}$ with Laplacian interaction of the form $\sum_iV(\Delta\varphi_i)$, where $\Delta$ is the discrete Laplacian and the potential $V(\cdot)$ is symmetric and uniformly strictly…
We consider the Lattice Gaussian free field in $d+1$ dimensions, $d=3$ or larger, on a large box (linear size $N$) with boundary conditions zero. On this field two potentials are acting: one, that models the presence of a wall, penalizes…
We study the localization/delocalization phase transition in a class of directed models for a homogeneous linear chain attracted to a defect line. The self-interaction of the chain is of mixed gradient and Laplacian kind, whereas the…
The strip wetting model is defined by giving a (continuous space) one dimensionnal random walk $S$ a reward $\gb$ each time it hits the strip $\R^{+} \times [0,a]$ (where $a$ is a positive parameter), which plays the role of a defect line.…
The membrane model is a Gaussian interface model with a Hamiltonian involving second derivatives of the interface height. We consider the model in dimension $\mathsf{d}\ge4$ under the influence of $\delta$-pinning of strength $\varepsilon$.…
We consider two models for biopolymers, the $\nabla$ interaction and the $\Delta$ one, both with the Gaussian potential in the random environment. A random field $\varphi:{0,1,...,N}\rightarrow \Bbb{R}^d$ represents the position of the…
We consider the d-dimensional massless free field localized by a delta-pinning of strength e. We study the asymptotics of the variance of the field, and of the decay-rate of its 2-point function, as e goes to zero, for general Gaussian…
We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…
We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in…
This paper continues a study initiated in [34], on the localization transition of a lattice free field on $\mathbb Z^d$ interacting with a quenched disordered substrate that acts on the interface when its height is close to zero. The…
This paper provides a rigorous study of the localization transition for a Gaussian free field on $\mathbb{Z}^d$ interacting with a quenched disordered substrate that acts on the interface when the interface height is close to zero. The…
We provide a complete description of the low temperature wetting transition for the two dimensional Solid-On-Solid model. More precisely we study the integer-valued field $(\phi(x))_{x\in \mathbb Z^2}$, associated associated to the energy…
We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning…
We consider a generalization of the classical pinning problem for integer-valued random walks conditioned to stay non-negative. More specifically, we take pinning potentials of the form $\sum_{j\geq 0}\epsilon_j N_j$, where $N_j$ is the…
We studied the dynamics of a quasi-one-dimensional chain-like system of charged particles at low temperature, interacting through a screened Coulomb potential in the presence of a local constriction. The response of the system when an…
We study a Langevin equation describing non-equilibrium depinning and wetting transitions. Attention is focused on short-ranged attractive substrate-interface potentials. We confirm the existence of first order depinning transitions, in the…
We continue the study, initiated in [Giacomin and Lacoin, JEMS 2018], of the localization transition of a lattice free field $\phi=(\phi(x))_{x \in Z^d}$, $d\ge 3$, in presence of a quenched disordered substrate. The presence of the…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase…
We apply new techniques developed in a previous paper to the study of some surface effects in the 2D Ising model. We examine in particular the pinning-depinning transition. The results are valid for all subcritical temperatures. By duality…