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

@article{Singh2011CorrectionsTP, title={Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet}, author={Rajiv R. P. Singh and Jaan Oitmaa}, journal={Physical Review B}, year={2011}, volume={85} }

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 ${1\over 2}\log{3\over 2}\approx 0.20273$. 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…

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## References

SHOWING 1-10 OF 18 REFERENCES

### Statistical Mechanics of Periodic Frustrated Ising Systems

- Physics
- 1986

and survey.- One-dimensional frustrated Ising systems.- Two-dimensional frustrated Ising systems.- Three-dimensional frustrated Ising systems.- Conclusion.

### Proc

- Phys. Math. Soc. (Japan) 23, 1069
- 1941

### Phys

- Rev. Lett. 97, 187202 (2006); Phys. Rev. E 75, 061118 (2007); Phys. Rev. E 75, 061119
- 2007

### Phys

- Rev. Lett. 83, 3293
- 1999

### Phys

- Rev. B 84, 144435
- 2011

### Phys

- Rev. 102, 1008
- 1956

### For a review of star-graph expansions, see S. Mckenzie in Phase Transitions Cargese

- 1980

### Phys

- Rev. B 75, 092202
- 2007

### For a recent review of spin-ice see

- Rev. Mod. Phys
- 2010

### Phys

- Rev. 79, 357
- 1950