4 papers
Topological percolation on a square lattice
S. K. Nechaev, O. A. Vasilyev
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality clas…
Topological correlations in trivial knots: new arguments in support of the crumpled polymer globule
Sergei Nechaev, Oleg Vasilyev
We prove the fractal crumpled structure of collapsed unknotted polymer ring. In this state the polymer chain forms a system of densely packed folds, mutually separated in all scale…
Scaling of crossing probabilities for the q-state Potts model at criticality
O. A. Vasilyev
We present study of finite-size scaling and universality of crossing probabilities for the -state Potts model. Crossing probabilities of the Potts model are similar ones in perc…
Number of bonds in the site-diluted lattices: sampling and fluctuations
Lev N. Shchur, Oleg A. Vasilyev
We have calculated analytically the mean value and the variance of the number of bonds on the lattices of dimension for the given occupation of sites. We consider both kinds of…