相关论文: Universal Properties of Self-Avoiding Walks from T…
We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. The method is based on loop erasure and restoration, and does not require exact…
The 2d gauge theory on the lattice is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free…
We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks…
We study the Effective Field Theory of Large Scale Structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduce an apparent scale dependence for the leading order…
The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails,…
We analyze the $1/\theta$ and 1/N expansions of the Wilson loop averages $<W(C)>_{U_\theta (N)}$ in the two-dimensional noncommutative $U_\theta (N)$ gauge theory with the parameter of noncommutativity $\theta$. For a generic rectangular…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
We consider the optimal paths in a $d$-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential.…
We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations ~r^{-a} for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We…
We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…
In order to study long chain polymers many lattice models accommodate a pulling force applied to a particular part of the chain, often a free endpoint. This is in addition to well-studied features such as energetic interaction between the…
The two-dimensional Hubbard model is studied for small values of the interaction strength (U of the order of the hopping amplitude t), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz,…
The average of two Wilson loops is expressed in terms of gauge invariant field strength correlators. Assuming the existence of finite correlation length $T_g$ and taking into account the absence of a fixed direction in colour space, we…
We consider a self-avoiding walk model (SAW) on the faces of the square lattice $\mathbb{Z}^2$. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square…
Numerical studies support the conjecture that in continuum planar QCD the eigenvalue density of a Wilson loop operator undergoes a transition as the loop is dilated while keeping the loop shape fixed. A second part of the conjecture is that…
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices,…
We present results of micron - resolution measurements of the ground motions in large particle accelerators over the range of spatial scales L from several meters to tens of km and time intervals T from minutes to several years and show…
We discuss the origin of the leg factors appearing in 2D string theory. Computing in the world sheet framework we use the semiclassical method to study string amplitudes at high energy. We show that in the case of a simplest 2-point…