Abstract
Quite a long time ago Yang and Lee [1] pointed out the importance of the relationship between the zeros of the partition function and the singularities of thermodynamic quantities occuring in a second order phase transition. They also proved the theorem that for the ferromagnetic Ising model these zeros lie on the unit circle in the complex activity plane z = exp(-2h/kT) where h is a complex symmetry breaking field and T is the temperature. In the thermodynamic limit they are distributed by some density g(h). Above TC this distribution has a gap around the real axis, which closes when approaching TC. Since g(h) is proportional to the spontaneous magnetization, the edges of this gap are branching points for the magnetization.
Permanent address: Institute of Physics of the University, Zagreb, Croatia, Yugoslavia
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952)
T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952)
See for example D. A. Kurtze, thesis and references therein.
D. A. Kurtze and M. E. Fisher, J. Stat. Phys. 19, 205 (1978)
G. A. Baker, M. E. Fisher and P. Moussa, Phys. Rev. Lett. 42, 615 (1979)
J. P. Kortman and R. B. Griffiths, Phys. Rev. Lett. 27, 1439 (1971)
D. A. Kurtze and M. E. Fisher, preprint
M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978)
P. Pfeuty, Ann. Phys. (N. Y.) 57 (1970)
M. Suzuki, Prog. Theor. Phys. 38, 1225 (1967) and
M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976)
R. Jullien, P. Pfeuty, J. N. Fields and S. Doniach, Phys. Rev. B 18, 3568 (1978) and see also refs. 3–13 in K. A. Penson, R. Jullien, P. Pfeuty, K. Uzelac, this conference
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Uzelac, K., Jullien, R., Pfeuty, P., Moussa, P. (1981). Yang-Lee Edge Singularity by Real Space Renormalization Group. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-81703-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81705-2
Online ISBN: 978-3-642-81703-8
eBook Packages: Springer Book Archive