Related papers: Random wetting transition on the Cayley tree : a d…
For the DNA denaturation transition in the presence of random contact energies, or equivalently the disordered wetting transition, we introduce a Strong Disorder Renewal Approach to construct the optimal contacts in each disordered sample…
We consider the critical point of two mean-field disordered models : (i) the Random Energy Model (REM), introduced by Derrida as a mean-field spin-glass model of $N$ spins (ii) the Directed Polymer of length $N$ on a Cayley Tree (DPCT) with…
In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse…
For Anderson localization on the Cayley tree, we study the statistics of various observables as a function of the disorder strength $W$ and the number $N$ of generations. We first consider the Landauer transmission $T_N$. In the localized…
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 study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices.These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the…
We consider a polymer, with monomer locations modeled by the trajectory of an underlying Markov chain, in the presence of a potential thatinteracts with the polymer when it visits a particular site 0. Disorder is introduced by having the…
In contrast to finite dimensions where disordered systems display multifractal statistics only at criticality, the tree geometry induces multifractal statistics for disordered systems also off criticality. For the Anderson tight-binding…
We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on…
The 'Cavity-Mean-Field' approximation developed for the Random Transverse Field Ising Model on the Cayley tree [L. Ioffe and M. M\'ezard, PRL 105, 037001 (2010)] has been found to reproduce the known exact result for the surface…
The spectral statistics of a Cayley-tree is numerically studied. The statistics are non-universal due to the high ratio of boundary sites. Once the boundary sites are connected to each other in a way that preserves the local structure of…
In this paper we develop the theory of drift-diffusion on a semi-infinite Cayley tree with stochastic resetting. In the case of a homogeneous tree with a closed terminal node and no resetting, it is known that the system undergoes a…
For the quantum Ising model with ferromagnetic random couplings $J_{i,j}>0$ and random transverse fields $h_i>0$ at zero temperature in finite dimensions $d>1$, we consider the lowest-order contributions in perturbation theory in…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible…
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…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
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…
We study the high-dimensional properties of an invading front in a disordered medium with random pinning forces. We concentrate on interfaces described by bounded slope models belonging to the quenched KPZ universality class. We find a…
We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by…