We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of ordering (quasi-long-range order) below a certain temperature...

We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen–Wang and Wolff cluster algorithms....

We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of the extended Harris criterion [A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413]...