Low-concentration series in general dimension

@article{Adler1990LowconcentrationSI,
  title={Low-concentration series in general dimension},
  author={Joan Adler and Yigal Meir and Amnon Aharony and A. Brooks Harris and Lior Klein},
  journal={Journal of Statistical Physics},
  year={1990},
  volume={58},
  pages={511-538}
}
We discuss recent work on the development and analysis of low-concentration series. For many models, the recent breakthrough in the extremely efficient no- free-end method of series generation facilitates the derivation of 15th-order series for multiple moments in general dimension. The 15th-order series have been obtained for lattice animals, percolation, and the Edwards-Anderson Ising spin glass. In the latter cases multiple moments have been found. From complete graph tables through to 13th… 

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References

SHOWING 1-10 OF 56 REFERENCES

Percolation in negative field and lattice animals.

We study in detail percolation in a negative ‘‘ghost’’ field, and show that the percolation model crosses over, in the presence of a negative field h, to the lattice-animal model, as predicted by the

Diffusion on percolating clusters.

This analysis provides the first analytic demonstration that the leading exponents γk are the same for a wide class of models, including the two types of ants as special cases, although corrections to scaling are larger for the myopic ant than for the blind one.

Series expansion evidence supporting the Alexander-Orbach conjecture in two dimensions

The authors extend the series expansion of Fisch and Harris (1978) for the resistive susceptibility chi R(p) by a further six terms on the square lattice. This leads to a more precise estimate of the

Resistance fluctuations in randomly diluted networks.

The resistance R(x,x’) between two connected terminals in a randomly diluted resistor network is studied on a d-dimensional hypercubic lattice at the percolation threshold pc and it is proved that ψ(q) is a convex monotonically decreasing function of q, which has the special valuesπ(0)=DB, ω(1)=ζR, and ψ (∞)=1/ν.

Dilute random-field Ising models and uniform-field antiferromagnets.

The order-parameter susceptibility χ of dilute Ising models with random fields and dilute antiferromagnets in a uniform field are studied for low temperatures and fields with use of low-concentration

Renormalized (1σ) expansion for lattice animals and localization

The use of the (1/σ) expansion to calculate the thermodynamic properties of systems such as the Ising model or percolation whose diagrammatic expansion contains only diagrams with no free ends is

Nonlinear resistor fractal networks, topological distances, singly connected bonds and fluctuations

The authors consider a fractal network of nonlinear resistors, with the voltage V behaving as a power of the current I, mod V mod =R mod I mod alpha . The resistance between two points at a distance

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Hydrodynamic dispersion in a self-similar geometry

The authors investigate the dispersion of a dynamically neutral tracer flowing in a self-similar, hierarchical model of a porous medium. They consider a purely convective limit in which the time for

Density of states on fractals : « fractons »

The density of states on a fractal is calculated taking into account the scaling properties of both the volume and the connectivity. We use a Green's function method developed elsewhere which
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