We present exact explicit expressions for the diagonal spin-spin correlation functions $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ in the $d=2$ Ising model, in terms of elliptic integrals, for $n$ up to 6. We also give a general structural formula for $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ and discuss its properties.We present exact explicit expressions for the diagonal spin-spin correlation functions $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ in the $d=2$ Ising model, in terms of elliptic integrals, for $n$ up to 6. We also give a general structural formula for $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ and discuss its properties.

Physical review. B, Condensed matterOct 1, 198424 citations

Correlation-function identities for general Ising models

R.J. Boel, Piet Kasteleyn

Physica A Statistical Mechanics and its ApplicationsSep 1, 19788 citations

We present exact explicit expressions for the diagonal spin-spin correlation functions $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ in the

d=2

Ising model, in terms of elliptic integrals, for

n

up to 6. We also give a general structural formula for $〈{\ensuremath{\sigma}}_{00}{\ensuremath{\sigma}}_{\mathrm{nn}}〉$ and discuss its properties.