Related papers: Universality in marginally relevant disordered sys…
We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…
Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and…
Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The…
The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of…
The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi one-dimensional disordered conductors in the unitary symmetry class is employed to calculate all $m$-point correlation functions by a generalization of the method of…
We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…
We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…
I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the \textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
The statistical mechanics of directed line-like objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-$T_{\tiny C}$ superconductors bears a close…
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…
Many low temperature disordered systems are expected to exhibit Poisson-Dirichlet (PD) statistics. In this paper, we focus on the case when the underlying disorder is a logarithmically correlated Gaussian process $\phi_N$ on the box…
We consider the directed polymer model in the weak disorder phase under the assumption that the partition function is $L^p$-bounded for some $p>1+\frac{2}d$. We prove that the point-to-point partition function can be approximated by two…
Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy on the invariant degree of polymerization…
We prove disorder universality of chaos phenomena and ultrametricity in the mixed p-spin model under mild moment assumptions on the environment. This establishes the long-standing belief among physicists that the Parisi solution in…
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…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
Disordered systems are very rich laboratories for exploring complex systems. In particular, disordered magnetic systems have been extremely important in the last five decades for understanding a wide range of phenomena. In this work, we use…