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Nuclear Physics B

The renormalization group analysis of the spin-spin correlation function in the two-dimensional Ising model

Hidenori Sonoda

Published Apr 1, 1991• 5 citations
Publisher
DOI
10.1016/0550-3213(91)90101-3

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A recent Monte Carlo renormalization-group study of the two-dimensional kinetic Ising model is extended to obtain renormalized time correlation functions from initial lattices of 16 \ifmmode\times\else\texttimes\fi{} 16 and 32 \ifmmode\times\else\texttimes\fi{} 32 spins. Different ways to estimate the dynamical exponent zzz are discussed, with our "best" estimate of $z\ensuremath{\simeq}2.23$ being consistent with the original study.
We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as $\ensuremath{\sim}{r}^{\ensuremath{-}a}$. Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for 0.995<a<20.995<a<20.995<a<2 and is characterized by the correlation length exponent $\ensuremath{\nu}=2/a+O({(2\ensuremath{-}a)}^{3})$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\ensuremath{\eta}}_{2}=1/2\ensuremath{-}(2\ensuremath{-}a)/4+O({(2\ensuremath{-}a)}^{2})$.