Related papers: Directed Polymers with Random Interaction : An Exa…
The overlap of a $d+1$ dimensional directed polymer of length $t$ in a random medium is studied using a Renormalization Group approach. In $d>2$ it vanishes at $T_c$ for $t\rightarrow \infty$ as $t^{\Sigma}$ where…
The transition from a weak-disorder (diffusive phase) to a strong-disorder (localized phase) for directed polymers in a random environment is a well studied phenomenon. In the most common setup, it is established that the phase transition…
We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…
Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two…
For the directed polymer in a random environment (DPRE), two critical inverse-temperatures can be defined. The first one, $\beta_c$, separates the strong disorder regime (in which the normalized partition function $W^{\beta}_n$ tends to…
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…
Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP…
We introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
The phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the $q\to 1$ limit of an extension of the $q-$ states Potts model.…
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 this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $\delta-$function potential. An exact formula of the so-called second moment of…
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 study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel…
The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization group method. With the aid of the mapping to the noisy-Burgers'…
The two-level correlation function $R_{d,\beta}(s)$ of $d$-dimensional disordered models ($d=1$, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ($\beta=1$)…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
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…