Energy Spectrum for the System of N Ising Spins with Identical Spin-Spin Coupling K/N - Anatomy of Phase Transition

• Authors: A. Czachor
• Languages of publication: EN

Abstracts

EN

For the Kittel-Shore-Kac interspin coupling K/N between N Ising spins the ferromagnetic phase transition in specific heat vs. T plot has appeared in literature as a purely mathematical phenomenon, via the exact calculation of the sum of states Z(T) and subsequent differentiations with respect to temperature T. Physical nature of the transition remains in such derivation invisible. As it is expected to be related to the interaction/temperature competition in populating energy levels of the system, in this paper we construct the density of energy states D(E) (or energy spectrum) of such systems, both for the ferromagnetic (K>0) and antiferromagnetic (K<0) coupling between spins. This allows one to see the essence of the difference between these systems as related to the discrete vs. quasi-continuous shape of the spectra at low energy states.

Keywords

EN

75.50.Kj; 65.40.-b

Discipline

• 65.40.-b: Thermal properties of crystalline solids
• 75.50.Kj: Amorphous and quasicrystalline magnetic materials

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2008
• Volume: 113
• Issue: 4
• Pages: 1161-1169

Dates

published

2008-04

received

2007-06-03

Contributors

author

A. Czachor

• Institute of Atomic Energy, Świerk, 05-400 Otwock, Poland

References

• 1. C. Kittel, H. Shore, Phys. Rev. A 138, 1165 (1965)
• 2. H. Al-Wahsh, M. Urban, A. Czachor, J. Magn. Magn. Mater. 185, 144 (1998)
• 3. A.J. van der Sijs, Phys. Rev. B 48, 7125 (1993)
• 4. M. Kac, in: Statistical Physics, Phase Transitions and Superfluidity, Eds. M. Chretien, E.P. Gross, S. Desser, Vol. 1, Gordon and Breach, New York 1968, p. 241
• 5. L. Landau, E. Lifshitz, Statistical Physics, PWN, Warszawa 1959 (in Polish)
• 6. R.H. Brout, in Ref. [4], p. 3
• 7. G.H. Wannier, Elements of Solid State Physics, The University Press, Cambridge 1959

Identifiers

DOI

10.12693/APhysPolA.113.1161