Related papers: Delocalization in random polymer models
We study the local eigenvalue statistics (LES) associated with one-dimensional lattice models of random polymers. We consider models constructed from two polymers. Each polymer is a finite interval of lattice points with a finite potential.…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase…
The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal…
We study the dimer model on the square grid, with quenched random edge weights. Randomness is chosen to have a layered structure, similar to that of the celebrated McCoy-Wu disordered Ising model. Disorder has a highly non-trivial effect…
The generalized copolymer model is a disordered system built on a discrete renewal process with inter-arrival distribution that decays in a regularly varying fashion with exponent $1+ \alpha\geq 1$. It exhibits a localization transition…
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…
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 a general model of a heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that the monomer units interact with the…
The Kronig-Penney model with random Dirac potentials on the lattice $\ZM$ has critical energies at which the Lyapunov exponent vanishes and the density of states has a van Hove singularity. This leads to a non-trivial quantum diffusion even…
We consider the position of the deconfining critical endpoint, where the first order transition for deconfinement is washed out by the presence of massive, dynamical quarks. We use an effective matrix model, employed previously to analyze…
We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the…
In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of…
This paper leads with a random polymer model in $\Z^2$ having long-range self-repulsive interactions. By comparison with a long range one-dimensional ferromagnetic Ising model we shown that the polymer models we considered here undergo a…
We consider a polymer with configuration modelled by the trajectory of a Markov chain, interacting with a potential of form $u+V_n$ when it visits a particular state 0 at time $n$, with $\{V_n\}$ representing i.i.d. quenched disorder. There…
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…
For a generalized Su-Schrieffer-Heeger model the energy zero is always critical and hyperbolic in the sense that all reduced transfer matrices commute and have their spectrum off the unit circle. Disorder driven topological phase…