The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $\beta \approx 3.6$ and $\beta_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^{\omega}$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $\omega \approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J. Phys.

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure

Fully parallel 3D thinning algorithms based on sufficient conditions for topology preservation

This paper presents a family of parallel thinning algorithms for extracting medial surfaces from 3D binary pictures. The proposed algorithms are based on sufficient conditions for 3D parallel reduction operators to preserve topology for (26, 6) pictures. Hence it is self-evident that our algorithms are topology preserving. Their efficient implementation on conventional sequential computers is also presented

A 3D 3-subiteration thinning algorithm for medial surfaces

Abstract. Thinning on a binary picture is an iterative layer by layer erosion to extract a reasonable approximation to its skeleton.This paper presents an efficient 3D parallel thinning algorithm which produces medial surfaces.Three–subiteration directional strategy is proposed: each iteration step is composed of three parallel subiterations according to the three deletion directions.The algorithm makes easy implementation possible, since deletable points are given by matching templates containing twentyeight elements.The topological correctness of the algorithm for (26, 6) binary pictures is proved.