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- W2091569475 abstract "The use of the ($frac{1}{ensuremath{sigma}}$) 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 reviewed. Here $ensuremath{sigma}=zensuremath{-}1$, where $z$ is the coordination number of the lattice. For more general problems we formulate a self-consistency condition for a site potential $h$, so that diagrams with free ends are eliminated. Construction of $h$ gives the leading order in ($frac{1}{ensuremath{sigma}}$) solution and is exact for the Cayley tree. We obtain correction terms by using a bond renormalized interaction so that to order ${(frac{1}{ensuremath{sigma}})}^{5}$ we need only consider two-site problems. Results are given for (1) ${K}_{c}$, the critical fugacity for animals, when either $H$, the fugacity for free ends, or $Q$, the density of free ends, is fixed, and (2) ($frac{t}{{E}_{c}}$), where ${E}_{c}$ is the mobility energy and $t$ is the magnitude of the hopping matrix element whose sign is random. At $d=8$ our results appear to be accurate to within about 0.01% for both animals and localization. We also obtain an expansion for $frac{Q({K}_{c})}{(z{K}_{c})}$ whose divergence near spatial dimensionality $d=4$ supports the idea that the order-parameter exponent $ensuremath{beta}$ for lattice animals passes through zero at $d=4$." @default.
- W2091569475 created "2016-06-24" @default.
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- W2091569475 date "1982-07-01" @default.
- W2091569475 modified "2023-09-27" @default.
- W2091569475 title "Renormalized (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:mfrac></mml:math>) expansion for lattice animals and localization" @default.
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- W2091569475 doi "https://doi.org/10.1103/physrevb.26.337" @default.
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