10 research outputs found
Probability of Incipient Spanning Clusters in Critical Two-Dimensional Percolation
The probability of simultaneous occurence of at least k spanning clusters has
been studied by Monte Carlo simulations on the 2D square lattice at the bond
percolation threshold Pc=1/2. The calculated probabilities for free boundary
conditions and periodic boundary conditions are in a very good coincidence with
the exact formulae developed recently by Cardy.Comment: Contribution to Lattice 97, LaTeX, 3 pages, 4 figures (1-eps, 3-
LaTeX
The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
We present a new way of probing the universality class of the site-diluted
two-dimensional Ising model. We analyse Monte Carlo data for the magnetic
susceptibility, introducing a new fitting procedure in the critical region
applicable even for a single sample with quenched disorder. This gives us the
possibility to fit simultaneously the critical exponent, the critical amplitude
and the sample dependent pseudo-critical temperature. The critical amplitude
ratio of the magnetic susceptibility is seen to be independent of the
concentration of the empty sites for all investigated values of . At the same time the average effective exponent is found
to vary with the concentration , which may be argued to be due to
logarithmic corrections to the power law of the pure system. This corrections
are canceled in the susceptibility amplitude ratio as predicted by theory. The
central charge of the corresponding field theory was computed and compared well
with the theoretical predictions.Comment: 6 pages, 4 figure
Specific heat of two-dimensional diluted magnets
Using Monte Carlo techniques, the two-dimensional site-diluted Ising model is
studied. In particular, properties of the specific heat, its critical behaviour
and the emergence of a non-singular maximum above the transition temperature at
moderate concentration of defects, are discussed.Comment: 10 pages, 5 eps-figures, elsart-style, submitted to Physica
Morphological diagram of diffusion driven aggregate growth in plane: competition of anisotropy and adhesion
Two-dimensional structures grown with Witten and Sander algorithm are
investigated. We analyze clusters grown off-lattice and clusters grown with
antenna method with and 8 allowed growth directions. With
the help of variable probe particles technique we measure fractal dimension of
such clusters as a function of their size . We propose that in the
thermodynamic limit of infinite cluster size the aggregates grown with high
degree of anisotropy () tend to have fractal dimension equal
to 3/2, while off-lattice aggregates and aggregates with lower anisotropy
() have . Noise-reduction procedure results in the
change of universality class for DLA. For high enough noise-reduction value
clusters with have fractal dimension going to when
.Comment: 6 pages, 8 figures, conference CCP201
Interfacial adsorption in Potts models on the square lattice
We study the effect of interfacial phenomena in two-dimensional perfect and
random (or disordered) -state Potts models with continuous phase
transitions, using, mainly, Monte Carlo techniques. In particular, for the
total interfacial adsorption, the critical behavior, including corrections to
scaling, are analyzed. The role of randomness is scrutinized. Results are
discussed applying scaling arguments and invoking findings for bulk critical
properties. In all studied cases, i.e., , , and , the spread
of the interfacial adsorption profiles is observed to increase linearly with
the lattice size at the bulk transition point.Comment: 6 pages, 6 eps figures, 1 table, minor corrections, accepted for
publication in Eur. Phys. J.
Interfacial adsorption in Potts models on the square lattice
We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) q-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., q = 3, 4, and q = 8, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point. © 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg