Related papers: Corrections to scaling in multicomponent polymer s…
The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $\omega$. The law of the simple symmetric random walk up to time $n$ is modified by the exponential of the sum of…
We calculate four-loop order corrections to the critical exponent $\eta$ in the two-field model of flat phase membranes. Obtained results show better agreement with the other calculation methods and confirm the validity of the perturbative…
We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\…
We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Bl\"ote and Nienhuis in J. Phys. A. {\bf 22}, 1415 (1989) and it describes polymers with some attraction, providing thus…
We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1 = nu omega <= 2, based upon Cardy's result for the critical crossing probability on an…
We explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of…
We present a Monte Carlo study of the one-component $\phi^4$ model on the cubic lattice in three dimensions. Leading order scaling corrections are studied using the finite size scaling method. We compute the corrections to scaling exponent…
We use complete enumeration and Monte Carlo techniques to study self--avoiding walks with random nearest--neighbor interactions described by $v_0q_iq_j$, where $q_i=\pm1$ is a quenched sequence of ``charges'' on the chain. For equal numbers…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for…
Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the…
We study a single flexible chain molecule grafted to a membrane which has pores of size slightly larger than the monomer size. On both sides of the membrane there is the same solvent. When this solvent is good, i.e. when the polymer is…
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…
We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point…
We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered…
A new Monte Carlo method for computing thermodynamical properties of very large polyelectrolytes is presented. It is based on a renormalization group relating the original polymer to a smaller system, where in addition to the naively…
We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions…
The number $n_s$ of clusters (per site) of size $s$, a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\simeq s^{-\tau}\, A\, (1+B s^{-\Omega})$. For the Fortuin--Kasteleyn…