480
8 Electric and Magnetic Phenomena
18. Show that the correlation function g(r) can be expressed in the form given
in Eq. (8.6.18b) and show that the correlation length ξ behaves as e 2βJ /2 for
temperatures approaching zero.
References
1. P.W. Atkins, R.S. Friedman, Molecular Quantum Mechanics, 3rd edn. (Oxford University
Press, Oxford, 1997), Chapter 12. See also A.J. Stone, Theory of Intermolecular Forces, 2nd
edn. (Clarendon Press, Oxford, 2013)
2. J.M. Honig, Thermodynamics, 2nd edn. (Academic Press, San Diego, 1999), p. 493. More
detailed discussions of the thermodynamics of electric and magnetic systems can be found in
§§1.6(f,g), §1.7, and §§5.6–5.8 of this reference
3. V. Heine, Proc. Camb. Phil. Soc. 52(3), 546 (1956)
4. Y. Zimmels, Phys. Rev. E 52, 1452 (1995)
5. H.B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd edn. (Wiley, New
York, 1985). See especially Appendix B
6. A.B. Pippard, The Elements of Classical Thermodynamics (Cambridge University Press,
Cambridge, 1957)
7. F. Mandl, Statistical Physics, 2nd edn. (Wiley, Chichester, 1988)
8. G. Castellano, J. Magn. Magn. Mater. 260, 146 (2003)
9. J.S. Griffith, The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge,
1961)
10. D.W. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, Upper Saddle River, 1994)
11. D.A. McQuarrie, Quantum Chemistry, 2nd edn. (University Science Books, Sausalito, 2008)
12. The Wigner-Eckart theorem lies beyond the scope of our discussion, but is developed in most
standard advanced quantum mechanics texts and in all specialized texts on angular momentum:
see, for example, R.N. Zare, Angular Momentum. Understanding Spatial Aspects in Chemistry
and Physics (Wiley, New York, 1988)
13. H.L. Schläfer, G. Gliemann, Basic Principles of Ligand Field Theory (Wiley-Interscience,
London, 1969)
14. B.N. Figgis, M.A. Hitchman, Ligand Field Theory and Its Applications (Wiley-VCH, New
York, 2000)
15. J.H. Van Vleck, Phys. Rev. 31, 587 (1928)
16. A. Frank, Phys. Rev. 39, 119 (1932)
17. A. Münster, Statistical Thermodynamics, vol. II (Springer-Verlag, New York, 1974), Chapter
XIV. This work is often considered to be the ‘bible’ of statistical thermodynamics
18. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Dover Publications, New York,
2007), Chapter 7. Square-Lattice Ising Model
19. C.J. Thompson, Mathematical Statistical Mechanics (Princeton University Press, Princeton,
1972)
20. B.M. McCoy, T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, 1973)
21. G.A. Baker, Jr., Quantitative Theory of Critical Phenomena (Academic Press, New York, 1990)
22. L. Onsager, Phys. Rev. 65, 117 (1944)
23. S.G. Brush, Revs. Mod. Phys. 39, 883 (1967)
24. R.K. Pathria, Statistical Mechanics, 2nd edn., (Butterworths-Heinemann, Oxford, 1996). See
especially Chapters 11 and 12
25. H.A. Kramers, G.H. Wannier, Phys. Rev. 60, 252, 263 (1941)
8 Electric and Magnetic Phenomena
18. Show that the correlation function g(r) can be expressed in the form given
in Eq. (8.6.18b) and show that the correlation length ξ behaves as e 2βJ /2 for
temperatures approaching zero.
References
1. P.W. Atkins, R.S. Friedman, Molecular Quantum Mechanics, 3rd edn. (Oxford University
Press, Oxford, 1997), Chapter 12. See also A.J. Stone, Theory of Intermolecular Forces, 2nd
edn. (Clarendon Press, Oxford, 2013)
2. J.M. Honig, Thermodynamics, 2nd edn. (Academic Press, San Diego, 1999), p. 493. More
detailed discussions of the thermodynamics of electric and magnetic systems can be found in
§§1.6(f,g), §1.7, and §§5.6–5.8 of this reference
3. V. Heine, Proc. Camb. Phil. Soc. 52(3), 546 (1956)
4. Y. Zimmels, Phys. Rev. E 52, 1452 (1995)
5. H.B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd edn. (Wiley, New
York, 1985). See especially Appendix B
6. A.B. Pippard, The Elements of Classical Thermodynamics (Cambridge University Press,
Cambridge, 1957)
7. F. Mandl, Statistical Physics, 2nd edn. (Wiley, Chichester, 1988)
8. G. Castellano, J. Magn. Magn. Mater. 260, 146 (2003)
9. J.S. Griffith, The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge,
1961)
10. D.W. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, Upper Saddle River, 1994)
11. D.A. McQuarrie, Quantum Chemistry, 2nd edn. (University Science Books, Sausalito, 2008)
12. The Wigner-Eckart theorem lies beyond the scope of our discussion, but is developed in most
standard advanced quantum mechanics texts and in all specialized texts on angular momentum:
see, for example, R.N. Zare, Angular Momentum. Understanding Spatial Aspects in Chemistry
and Physics (Wiley, New York, 1988)
13. H.L. Schläfer, G. Gliemann, Basic Principles of Ligand Field Theory (Wiley-Interscience,
London, 1969)
14. B.N. Figgis, M.A. Hitchman, Ligand Field Theory and Its Applications (Wiley-VCH, New
York, 2000)
15. J.H. Van Vleck, Phys. Rev. 31, 587 (1928)
16. A. Frank, Phys. Rev. 39, 119 (1932)
17. A. Münster, Statistical Thermodynamics, vol. II (Springer-Verlag, New York, 1974), Chapter
XIV. This work is often considered to be the ‘bible’ of statistical thermodynamics
18. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Dover Publications, New York,
2007), Chapter 7. Square-Lattice Ising Model
19. C.J. Thompson, Mathematical Statistical Mechanics (Princeton University Press, Princeton,
1972)
20. B.M. McCoy, T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, 1973)
21. G.A. Baker, Jr., Quantitative Theory of Critical Phenomena (Academic Press, New York, 1990)
22. L. Onsager, Phys. Rev. 65, 117 (1944)
23. S.G. Brush, Revs. Mod. Phys. 39, 883 (1967)
24. R.K. Pathria, Statistical Mechanics, 2nd edn., (Butterworths-Heinemann, Oxford, 1996). See
especially Chapters 11 and 12
25. H.A. Kramers, G.H. Wannier, Phys. Rev. 60, 252, 263 (1941)