Abstract
With the aid of the differential real-space method we derive exact renormalization group (RG) equations for the Gaussian model ind dimensions. The equations involved + 1 spatially dependent nearest-neighbor interactions. We locate a critical fixed point and obtain the exact thermal critical indexy T = 2. A special trajectory of the full nonlinear RG transformation is found and the free energy of the corresponding initial state calculated.
Similar content being viewed by others
References
H. J. Hilhorst, M. Schick, and J. M. J. van Leeuwen,Phys. Rev. Lett. 40:1605 (1978).
H. J. Hilhorst, M. Schick, and J. M. J. van Leeuwen,Phys. Rev. B 19:2749 (1979).
Th. Niemeijer and J. M. J. van Leeuwen, inPhase Transitions and Critical Phenomena, C. Domb and M. S. Green, eds. (Academic, London, 1976), Vol. 6.
H. J. F. Knops and H. J. Hilhorst,Phys. Rev. B 19:3689 (1979).
W. van Saarloos, J. M. J. van Leeuwen, and A. L. Stella,Physica 97A:319 (1979).
Y. Yamazaki and H. J. Hilhorst,Phys. Lett. 70A:329 (1979).
Y. Yamazaki, H. J. Hilhorst, and G. Meissner,Z. Physik B 35:333 (1979).
R. Dekeyser and A. Stella, to be published.
I. Syozi, inPhase Transitions and Critical Phenomena, C. Domb and M. S. Green, eds. (Academic, London, 1972), Vol. 1.
J. M. J. van Leeuwen, private communication.
L. P. Kadanoff, A. Houghton, and M. C. Yalabik,J. Stat. Phys. 14:171 (1976).
Author information
Authors and Affiliations
Additional information
Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 130 Ferroelektrika.
Rights and permissions
About this article
Cite this article
Yamazaki, Y., Hilhorst, H.J. & Meissner, G. Differential real-space renormalization of thed-Dimensional Gaussian model. J Stat Phys 23, 609–625 (1980). https://doi.org/10.1007/BF01011732
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011732