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We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several…

Soft Condensed Matter · Physics 2015-05-13 Hans-Karl Janssen , Frank Wevelsiep , Olaf Stenull

When $d\ge 3$, the directed polymer a in random environment on $\mathbb Z^d$ is known to display a phase transition from a diffusive phase, known as \textit{weak disorder} to a localized phase, referred to as \textit{strong disorder}. This…

Probability · Mathematics 2025-05-20 Hubert Lacoin

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…

Statistical Mechanics · Physics 2009-11-07 Peter Grassberger , Hsiao-Ping Hsu

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…

Condensed Matter · Physics 2009-10-28 Sutapa Mukherji , Somendra M. Bhattacharjee , A. Baumgärtner

We study the Directed Polymer model subject to a particular form of disorder, $\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice…

Statistical Mechanics · Physics 2009-10-31 Paolo De Los Rios , Yi-Cheng Zhang

The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario…

Statistical Mechanics · Physics 2009-11-07 Roya Mohayaee , Attilio L. Stella , Carlo Vanderzande

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…

Statistical Mechanics · Physics 2013-05-29 Tom Alberts , Kostya Khanin , Jeremy Quastel

We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for…

Condensed Matter · Physics 2009-07-10 Kay Joerg Wiese , Pierre Le Doussal

We consider the drift of a polymer chain in a disordered medium, which is caused by a constant force applied to the one end of the polymer, under neglecting the thermal fluctuations. In the lowest order of the perturbation theory we have…

Soft Condensed Matter · Physics 2009-10-31 Semjon Stepanow , Michael Schulz

Building on and from the work of Brydges and Imbrie, we give an elementary calculation of the volume of the space of branched polymers of order $n$ in the plane and in 3-space. Our development reveals some more general identities, and…

Probability · Mathematics 2007-09-17 Richard Kenyon , Peter Winkler

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…

Mathematical Physics · Physics 2007-05-23 John Z. Imbrie

We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization…

Condensed Matter · Physics 2016-08-31 Hyoungsoo Yoon , J. M. Deutsch

We study the question of how the competition between $\textit{bulk disorder}$ and a $\textit{localized microscopic defect}$ affects the macroscopic behavior of a system in the directed polymer context at the free energy level. We consider…

Probability · Mathematics 2018-04-04 Neal Madras , Gökhan Yıldırım

We present a unifying picture of the compact, dense and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute case. In…

Statistical Mechanics · Physics 2007-05-23 Jesper Lykke Jacobsen , Jane' Kondev

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…

Disordered Systems and Neural Networks · Physics 2009-11-11 F. L. Toninelli

We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…

Statistical Mechanics · Physics 2012-10-03 Elisabeth Agoritsas , Sebastian Bustingorry , Vivien Lecomte , Gregory Schehr , Thierry Giamarchi

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model…

Statistical Mechanics · Physics 2015-05-14 Hans-Karl Janssen , Olaf Stenull

By tracking small particles in the bulk of an intensely turbulent flow, we show that even a very small concentration of long-chain polymers disrupts the usual turbulent energy cascade. The polymers affect scales much larger than their…

Fluid Dynamics · Physics 2007-12-31 Nicholas T. Ouellette , Haitao Xu , Eberhard Bodenschatz

We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…

Probability · Mathematics 2018-06-01 Quentin Berger , Niccolo Torri

It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…

Statistical Mechanics · Physics 2016-10-12 Bernard Derrida , Peter Mottishaw