Related papers: Zero temperature limit for (1+1) directed polymers…
Effective pair interactions with a soft-repulsive component are a well-known feature of polymer solutions and colloidal suspensions, but they also provide a key to interpret the high-pressure behaviour of simple elements. We have computed…
We study the stability of the glassy equilibrium state of a directed polymer in random media against weak perturbations including the intriguing problem of temperature-chaos. The statistical correlation of two real replica systems under…
We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
Classical particle motions in an inverse harmonic potential show the exponential sensitivity to initial conditions, where the Lyapunov exponent $\lambda_L$ is uniquely fixed by the shape of the potential. Hence, if we naively apply the…
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…
We uncover a nontrivial signature of the hierarchical structure of quasi-degenerate random directed polymers (RDPs) at zero temperature in 1+1 dimensional lattices. Using a cylindrical geometry with circumference $8 \leq W \leq 512$, we…
We study the directed polymer model in a bounded environment in weak disorder but without $L^2$-boundedness, specifically the speed of homogenization for the field $(W_n^{0,x})_{x\in\mathbb Z^d}$, where $W_n^{0,x}$ denotes the associated…
We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic…
We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a>0. We say a chain is formed…
Exact bounds are obtained for the quenched free energy of a polymer with random hydrophobicities in the presence of an interface separating a polar from a non polar solvent. The polymer may be ideal or have steric self-interactions. The…
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 compute the leading and next--to--leading corrections to the finite temperature scalar potential for a 3+1 dimensional $\phi^4$ theory using a systematic $1/N$ expansion. Our approach automatically avoids problems associated with…
The relaxational dynamics of 1+1 dimensional directed polymer in random potential is studied by Monte Carlo simulation. A series of temperature quench experiments is performed changing waiting times. Clear crossover from quasi-equilibrium…
We show that if the normalized partition function $W^{\beta}_n$ of the directed polymer model on $\mathbb Z^d$ converges to zero, then it does so exponentially fast. This implies that there exists a critical value $\beta_c$ for the inverse…
We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is…
We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder is introduced by, for example, having the…
We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each…
The log-partition function $ \log W_N(\beta)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime…