A Use of Bethe Lattice Solutions for Percolation-Constrained Phenomena

概要

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Classes of phenomena are considered that are strongly influenced by percolation constraints in particular showing a critical percolation concentration for some value P_c of a 'concentration' parameter P. Using this feature an attempt is made to generate useful approximations to behaviour in real lattices over a complete concentration range from exact solutions available in simple pseudo-lattices-here only Bethe lattices are used. Fitting Bethe solutions at P=P_c and P=1 is found to give a numerically useful interpolation for an P in a range of lattices and for several problems; detailed comparisons with best available data are given for(quenched)dilute Ising ferromagnets, random resistor networks and spin-wave stiffness constants. Limitations of the approach are emphasised numerically-especially the inadequate distinction between bond and site problems or treatment of critical exponents. It is also suggested that localization in cellularly disordered lattices might be amenable to a similarly motivated approach.
一般社団法人日本物理学会の論文
1975-01-25