Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions
An exact method for determining the critical percolation probability, pc, for a number of two‐dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc…
Excluded-Volume Problem and the Ising Model of Ferromagnetism
The relationship between the excluded-volume problem for a discrete random walk on a lattice and the corresponding Ising model of ferromagnetism is investigated. Systematic methods are presented for…
On the susceptibility of a ferromagnetic above the Curie point
Series expansions for the susceptibility of a ferromagnetic at high temperatures are examined in detail to estimate the curvature of the reciprocal of the susceptibility immediately above the Curie…
Percolation processes in two dimensions. I. Low-density series expansions
The derivation of low-density series expansions for the mean cluster size in random site and bond mixtures on a two-dimensional lattice is described briefly. New data are given for the triangular,…
Percolation processes in d-dimensions
Series data for the mean cluster size for site mixtures on a d-dimensional simple hypercubical lattice are presented. Numerical evidence for the existence of a critical dimension for the cluster…
Percolation processes in two dimensions. V. The exponent δp and scaling theory
For pt.IV see ibid., vol.9, p.725 (1976). By introducing a notional field variable lambda into the percolation problem, a function Pc( lambda ) is defined whose Ising analogue is the magnetic field…
Susceptibility and fourth-field derivative of the spin-1/2 Ising model for T>Tc and d=4
- D. Gaunt, M. Sykes, S. McKenzie
- Physics
- 1 June 1979
THe authors investigate the spin-1/2 Ising model with nearest-neighbour interactions on the four-dimensional simple hypercubic lattice. High-temperature series expansions are studied for the…
A note on the mean size of clusters in the Ising model
The derivation of series expansions for the mean size of finite clusters in the Ising model is described briefly. From the analysis of low temperature series it is concluded that for a…
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