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At least 919 records · Page 51Linked to original sources
PubMed1999

Ground-state degeneracy of Potts antiferromagnets on two-dimensional lattices: approach using infinite cyclic strip graphs.

The q-state Potts antiferromagnet on a lattice Lambda exhibits nonzero ground-state entropy S0=kB ln W for sufficiently large q and hence is an exception to the third law of thermodynamics. An outstanding challenge has been the calculation of W(sq,q) on the square (sq) lattice. We present here an exact calculation of W on an infinite-length cyclic strip of the square lattice, which embodies the expected analytic properties of W(sq,q). Similar results are given for the kagomé lattice.

Journal Article↗
PubMed2002

Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation.

We consider the fractal dimensions d(k) of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions x(k)=2-d(k) describe the asymptotic decay of the probabilities P(r,R) approximately (r/R)(x(k)) that an annulus of radii r<<1 and R>>1 is traversed by k disjoint paths, all living on the percolation clusters. Using a transfer matrix approach, we obtain numerical results for x(k), k<or=6. They are well fitted by the ansatz x(k)=1 / 12k(2)+1 / 48k+(1-k)C, with C=0.0181+/-0.0006.

Journal Article↗
PubMed2004

Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights.

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Phys. Rev. Lett. 89, 258702 (2002)]. Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.

Journal Article↗