相关论文: Universal Properties of Self-Avoiding Walks from T…
From the low-energy effective theory of dilatons, consistent with the scale anomaly, we calculate the $2\to2$ scattering amplitudes of dilatons. We find that the one-loop amplitude violates the unitarity bound as the scattering energy…
If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks…
We observed the conformation of threads that free released from different altitudes. We also explore the effect of wetting liquid on the conformation developed. When released from an altitude, the thread conformation changes when free…
This is an exposition of the theorem from the title, which says that the number of self-avoiding walks with n steps in the hexagonal lattice has asymptotics (2cos(pi/8))^{n+o(n)}. We lift the key identity to formal level and simplify the…
We put forward a general field theory for membranes with embedded activators and analyse their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic…
We study the path behaviour of a simple random walk on the 2-dimensional comb lattice ${\mathbb C}^2$ that is obtained from ${\mathbb Z}^2$ by removing all horizontal edges off the x-axis. In particular, we prove a strong approximation…
A generalised model for interacting self-avoiding trails on the square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and…
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they…
We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result \cite{ref:Has07}. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
It is shown that the effective string recently introduced to describe the long distance dynamics of 3D gauge systems in the confining phase has an intriguing description in terms of models of 2D self-avoiding walks in the dense phase. The…
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…
In this paper we extend the study initiated in arXiv:2302.04709v2 [hep-th] to the computation of one-loop elastic amplitudes. We consider 1+1 dimensional massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic…
Many diffusive systems involve correlated random walkers due to a shared environment. Such systems can be modeled as random walks in random environments (RWRE). These models differ from classical diffusion in the behavior of the extremes --…
We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean…
We continue the program [1] of carving out the space of large $N$ confining gauge theories by modern S-matrix bootstrap methods, with the ultimate goal of cornering large $N$ QCD. In this paper, we focus on the effective field theory of…
A set of general allometric scaling laws is derived for different systems represented by tree networks. The formulation postulates self-similar networks with an arbitrary number of branches developed in each generation, and with an…
It has been shown recently that the amplitude of the creation of $n$ real scalar particles by one virtual boson near $n$--particle threshold exhibits exponential behavior at $n\sim1/\lambda$. We extend this result to the processes of…
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in…
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $\Phi^h$ interaction in d…