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We study corrections to single tetrahedron based approximations for theentropy, specific heat and uniform susceptibility of the pyrochlore latticeIsing antiferromagnet, by a Numerical Linked Cluster (NLC) expansion. In atetrahedron based NLC, the first order gives the Pauling residual entropy of${1\over 2}\log{3\over 2}\approx 0.20273$. A 16-th order NLC calculationchanges the residual entropy to 0.205507 a correction of 1.37 percent over thePauling value. At high temperatures, the accuracy of the calculations isverified by a high temperature series expansion. We find the corrections to thesingle tetrahedron approximations to be at most a few percent for all thethermodynamic properties.

Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet