arXiv subjects

S. B. Santra

Publications and source records attributed to S. B. Santra.

21 records · Page 2Linked to original sources

arXiv2004

Breakdown of Universality in Directed Spiral Percolation

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.

cond-mat.dis-nn↗

arXiv2004

Directed Spiral Percolation Hull on the Square and Triangular Lattices

Critical properties of hulls of directed spiral percolation (DSP) clusters are studied on the square and triangular lattices in two dimensions (2D). The hull fractal dimension ($d_H$) and some of the critical exponents associated with different moments of the hull size distribution function of the anisotropic DSP clusters are reported here. The values of $d_H$ and other critical exponents are found the same within error bars on both the lattices. The universality of the hull's critical exponents then holds true between the square and triangular lattices in 2D unlike the cluster's critical exponents which exhibit a breakdown of universality. The hull fractal dimension $(d_H \approx 1.46)$ is also found close to 4/3 and away from 7/4, that of ordinary percolation cluster hull. A new conjecture is proposed for the hull fractal dimension ($d_H$) in terms of two connectivity length exponents ($ν_\|$ $&$ $ν_\perp$) of the anisotropic clusters generated here. The values of $d_H$ and other critical exponents obtained here are very close to that of the spiral percolation cluster hull. The hull properties of the DSP clusters are then mostly determined by the rotational constraint and almost independent on the directional constraint present in the model.

cond-mat.dis-nn↗

arXiv2003

Directed Spiral Site Percolation on the Square Lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension $d_f\approx 1.733$. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as $p\to p_c$ with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution $P_s(p)$ show power law behavior with $|p-p_c|$ in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of $P_s(p)$. The results obtained are in good agreement with other model calculations.

cond-mat.soft↗