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Physical review. B, Condensed matter

Off-axis correlation functions in the isotropicd=2 Ising model

Robert E. Shrock, Ranjan K. Ghosh

Published Feb 1, 1985• 16 citations
Publisher

Abstract

We present exact explicit expressions for the spin-spin correlation functions 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 for (m,n)=(2,1), (3,1), (3,2), (4,1), (4,2), and (4,3) in the isotropic d=2 Ising model. We also infer a general structural formula for arbitrary 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{\ensuremath{\sigma}}}_{\mathrm{m}}$,n〉 in terms of complete elliptic integrals K and E.

DOI
10.1103/physrevb.31.1486

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For both T>TcT>{T}_{c}T>Tc​ and T<TcT<{T}_{c}T<Tc​, we report exact expressions for the nnn-spin correlation function of the two-dimensional Ising model suitable for studying large separations between spins. In particular, the scaling limit of these correlation functions can be shown to exist and yields nnn-point Schwinger functions of some relativistic quantum field theories.