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

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