Abstract
The critical behaviour of the energy density of the semi-infiniten-vector model is studied near the ordinary transition. The singularities near the free surface are analyzed with the help of renormalization-group methods and a short-distance expansion. The asymptotic behaviour at large distances from the surface and the thermal singularities of the energy density at the surface are also discussed. It is shown that the associated critical exponents can be expressed in terms of bulk exponents.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
See for example Ref. 8 Burkhardt, T.W., Eisenriegler, E.: Critical Phenomena near Free Surfaces and Defect Planes. Preprint (1980) and Phys. Rev. B (to appear)
Diehl, H.W., Dietrich, S.: Phys. Lett.80A, 408 (1980)
Diehl, H.W., Dietrich, S.: Z. Phys. B-Condensed Matter42, 65 (1981)
Diehl, H.W., Dietrich, S.: Phys. Rev. B (to appear)
Diehl, H.W., Dietrich, S., Eisenriegler, E.: (to be published)
The same model has been investigated by a variety of authors. Detailed references can be found in [3]
See for example: Bray, A.J., Moore, M.A.: J. Phys. A10, 1927 (1977)
Burkhardt, T.W., Eisenriegler, E.: Critical Phenomena near Free Surfaces and Defect Planes. Preprint (1980) and Phys. Rev. B (to appear)
Diehl, H.W., Dietrich, S.: (to be published)
Voorhoeve, R.J.H.: AIP Conference Proc, No18, pt. 1, 19 (1973)
Suhl, H.: Phys. Rev. B11, 2011 (1975)
Zimmermann, W.: In: Lectures on Elementary Particles and Quantum Field Theory. Deser, S., Grisaru, M., Pendleton, H. (eds.) Cambridge: MIT Press 1971
See also: Symanzik, K.: Small Distance Behaviour in Field Theory. In: Particles, Quantum Fields and Statistical Mechanics. Alexanian, M., Zapeda, A. (eds.), Berlin, Heidelberg, New York: Springer-Verlag 1975
The counterterms needed for 〈φ2〉 have also been discussed by Symanzik, K.: In: Desy preprint No. 81-004 and Nucl. Phys. B (to appear)
Kamke, E.: Differentialgleichungen, Lösungsmethoden und Lösungen. Bd. I, p. 16. New York: Chelsea Publishing Company 1971
Reed, P.: J. Phys. A11, 137 (1978)
Burkhardt and Eisenriegler [8] discuss also the critical behaviour of the energy density near a defect plane. They find that the energy density in the plane contains a term\( \sim t^{2 - \alpha - v - \Phi _{||}^{ord} } \) and a second one\( \sim t^{2 - \alpha - v - \gamma _{11}^{ord} } \) where\(\gamma _{11}^{ord} \) is the exponent for the local susceptibility. In the case of thed=3 Ising model (n=1) the exponents of the two powers differ only slightly since\(2\gamma _{11}^{ord} \simeq - v\).
McCoy, B., Wu, T.T.: Phys. Rev.162, 436 (1967)
An analogous example is discussed in: Itzykson, C., Zuber, J.-B.: Quantum Field Theory: New York: McGraw Hill 1980
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dietrich, S., Diehl, H.W. Critical behaviour of the energy density in semi-infinite systems. Z. Physik B - Condensed Matter 43, 315–320 (1981). https://doi.org/10.1007/BF01292798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01292798