Abstract
For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.
Similar content being viewed by others
References
Ring, P., Schuck, P.: The nuclear many body problem. Berlin, Heidelberg, New York: Springer 1980
Thouless, D.J.: Nucl. Phys.21, 225 (1960); ibid.22, 78 (1961)
Davis, E.D.: PhD-Thesis, Johannesburg 1986
Davis, E.D., Heiss, W.D.: J. Phys. G: Nucl. Phys.12, 805 (1986)
Glick, A.J., Lipkin, H.J., Meshkov, N.: Nucl. Phys.62, 199 (1965)
Agassi, D.: Nucl. Phys. A116, 49 (1968)
Agassi, D., Lipkin, H.J., Meshkov, N.: Nucl. Phys.86, 321 (1966)
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966
Yang, C.N., Lee, T.D.: Phys. Rev.87, 404 (1952)
Mang, H.-J.: Phys. Rev.18C, 325 (1975)
Seligmann, T.H., Nishioka, H. (eds.): Quantum chaos and statistical nuclear Physics. Lecture Notes in Physics 263. Berlin, Heidelberg, New York: Springer 1986
Zirnbauer, M.R., Verbaarschot, J.J.M., Weidenmüller, H.A.: Nucl. Phys. A411, 161 (1983)
Author information
Authors and Affiliations
Additional information
The author is indebted to P.G.L. Leach for numerous illuminating discussions. This paper has been completed while the author was visiting the theory group of the Max-Planck Institute for Nuclear Physics in Heidelberg. The kind hospitality and many discussions are gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Heiss, W.D. Exceptional points of a Hamiltonian and phase transitions in finite systems. Z. Physik A - Atomic Nuclei 329, 133–138 (1988). https://doi.org/10.1007/BF01283767
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01283767