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- W2048443823 abstract "An exact duality-decimation transformation is derived for a large class of two-dimensional spin systems on a square lattice. It maps a model with interactions in every second square (checkerboard interactions) onto a model with interactions in every square and vice versa. The transformation is applicable to Ising, Potts, solid-on-solid (SOS), and $xensuremath{-}y$ models. It may be used to reformulate the site percolation problem in terms of the $sensuremath{rightarrow}1$ limit of a Potts model with four-spin interactions in every elementary square. The transformation maps the van Beijeren SOS model, which is equivalent to the $F$ model, onto an $xensuremath{-}y$ model with checkerboard interactions. Thus one has an exactly soluble $xensuremath{-}y$ model, which, however, bears little resemblance to the ordinary $xensuremath{-}y$ model. The transformation may be combined with a bond-shifting approximation to obtain a real-space renormalization scheme which in some respects represents an improvement over the Migdal-Kadanoff formula. No nearest-neighbor bonds are shifted. Better values of the exponent $ensuremath{nu}$ are obtained for the Ising and Potts models. Apart from exponentially vanishing corrections, the renormalization transformation for SOS and $xensuremath{-}y$ models has a surface of fixed points corresponding to generalizations of the usual discrete Gaussian and Villain models." @default.
- W2048443823 created "2016-06-24" @default.
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- W2048443823 date "1979-10-01" @default.
- W2048443823 modified "2023-09-24" @default.
- W2048443823 title "Applications of an exact duality-decimation transformation for two-dimensional spin systems on a square lattice" @default.
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- W2048443823 doi "https://doi.org/10.1103/physrevb.20.2905" @default.
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