Related papers: Nested critical points for a directed polymer on a…
We show that the weak disorder phase for the directed polymer model in a bounded random environment is characterized by the integrability of the running supremum $\sup_{n\in \mathbb N}W_n^\beta$ of the associated martingale…
We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment…
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…
We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak…
We provide a comprehensive analysis of the two-parameter Beta distributions seen from the perspective of second-order stochastic dominance. By changing its parameters through a bijective mapping, we work with a bounded subset D instead of…
The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel~\cite{AKQ12}. It was proved that at inverse temperature $\beta n^{-\gamma}$ with $\gamma=1/4$ the partition function, centered…
We study an undirected polymer chain living on the 1-dimensional integer lattice and carrying i.i.d.\ random charges. Each self-intersection of the polymer contributes to the Hamiltonian an energy that is equal to the product of the charges…
In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using…
We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we present results about large deviations for directed polymers…
We continue with the study of the mollified stochastic heat equation in $d\geq 3$ given by $d u_{\epsilon,t}=\frac 12\Delta u_{\epsilon,t}+ \beta \epsilon^{(d-2)/2} \,u_{\epsilon,t} \,d B_{\epsilon,t}$ with spatially smoothened cylindrical…
We consider a polymer with configuration modeled by the path of a Markov chain, interacting with a potential $u+V_n$ which the chain encounters when it visits a special state 0 at time $n$. The disorder $(V_n)$ is a fixed realization of an…
For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…
Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of…
The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $\omega$. The law of the simple symmetric random walk up to time $n$ is modified by the exponential of the sum of…
We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of…
The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained…
The phase transition in the q-state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional…
We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer…
We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder is introduced by, for example, having the…
We study a directed coupled map lattice model in two dimensions, with two degrees of freedom associated with each lattice site. The two freedoms are coupled at a fraction $c$ of lattice bonds acting as quenched random defects. In the case…