# 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}
}
• Published 19 December 2011
• Physics
• Physical Review B
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…

## Figures from this paper

• Physics
Physical review letters
• 2021
A robust spontaneous inversion symmetry breaking is found, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments, and suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.
• Physics
• 2022
We investigate the ground-state properties of the nearest-neighbor S = 1 pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, density-matrix renormalization group (DMRG)
• Physics, Computer Science
Journal of Statistical Mechanics: Theory and Experiment
• 2022
This work estimates the residual entropy of ice Ih (ordinary ice) by an improvement of the Wang–Landau Monte Carlo algorithm, which directly calculates the density of states of the system.
• Physics
• 2020
We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore $S=\frac{1}{2}$ quantum antiferromagnet, at finite temperature
In this thesis we investigate a range of properties for spin ice under various perturbations theoretically. Diluted spin ices, Dy2−xYxTi2O7 and Ho2−xYxTi2O7, where the magnetic rare-earth ions Dy3+
• Physics
• 2015
In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features
• Physics
• 2022
Since the problem of the residual entropy of square ice was exactly solved, exact solutions for two-dimensional realistic ice models have been of interest. In this paper, we study the exact residual
• Physics
Physical Review B
• 2019
We present thermodynamic and neutron scattering measurements on the quantum spin ice candidate Nd$_2$Zr$_2$O$_7$. The parameterization of the anisotropic exchange Hamiltonian is refined based on
• Physics
Physical review letters
• 2018
Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, it is found that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantumspin liquid at a high-symmetry, SU(2) point.
Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has

## References

SHOWING 1-10 OF 18 REFERENCES

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

• 1980

### Phys

• Rev. B 75, 092202
• 2007

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

• Rev. Mod. Phys
• 2010

• Rev. 79, 357
• 1950