Related papers: Equality of critical points for polymer depinning …
Consider a Markov chain $(X_n)_{n\geqslant 0}$ with values in the state space $\mathbb X$. Let $f$ be a real function on $\mathbb X$ and set $S_0=0,$ $S_n = f(X_1)+\cdots + f(X_n),$ $n\geqslant 1$. Let $\mathbb P_x$ be the probability…
We introduce a random walk in random environment associated to an underlying directed polymer model in $1+1$ dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…
We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of propagating front of…
We present numerical evidence using Monte Carlo simulations of finite-temperature phase transition in two dimensional Coulomb Glass lattice model with random site energies at half-filling. For the disorder strengths ($W$) studied in this…
We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The…
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase…
We compare two order parameters for the deconfinement transition, induced by thermal and density effects, commonly used in the literature, namely the thermal and density evolution of the continuum threshold $s_{0}$, within the frame of the…
We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in…
We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and…
We present models where $\gamma_+$ and $\gamma_-$, the exponents of the susceptibility in the high and low temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete…
We report a careful finite size scaling study of the metal insulator transition in Anderson's model of localisation. We focus on the estimation of the critical exponent $\nu$ that describes the divergence of the localisation length. We…
In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of…
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for…
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…
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…
In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions…
The location of the critical end point (CEP) in the QCD phase diagram is determined under different scenarios. The effect of strangeness, isospin/charge asymmetry and an external magnetic field is investigated. The discussion is performed…
We consider the hermitian matrix model with an external field entering the quadratic term $\tr(\Lambda X\Lambda X)$ and Penner--like interaction term $\alpha N(\log(1+X)-X)$. An explicit solution in the leading order in $N$ is presented.…
We provide an introductory account of a tricritical phase diagram, in the setting of a mean-field random walk model of a polymer density transition, and clarify the nature of the density transition in this context. We consider a…