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We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $xi_parallel$ in the direction along defects, and a perpendicular correlation length $xi_perp$ in the direction perpendicular to the lines. Both $xi_parallel$ and $xi_perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $ u_parallel$ and $ u_perp$ take different values. This property is specific for anisotropic scaling and the ratio $ u_parallel/ u_perp$ defines the anisotropy exponent $theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $gamma$. Our results corroborate the renormalization group predictions obtained earlier.
Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY univ
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the probabilities of ga
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns
By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point