Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Bleher and Ya. Sinai: Critical indices for Dyson's asymptotically hierarchical models, Commun.Math.Phys. 45 (1973) 249–293.
P. Bleher and P. Major: Renormalization of Dyson's hierarchical vector valued φ4 model at low temperature, Commun.Math.Phys. 95 (1984) 487–532.
F. Dunlop and C. Newman: Multicomponent field theories and classical rotators, Commun.Math.Phys. 44 (1975) 223–235.
F.J. Dyson: An Ising ferromagnet with distributions of long range order, Commun.Math.Phys. 21 (1971) 269–283.
K. Gawedzki and A. Kupiainen: A rigorous block spin approach to massless lattice theories, Commun.Math.Phys. 77 (1980) 31–64.
K. Gawedzki and A. Kupiainen: Non-Gaussian fixed points of the block spin transformation, hierarchical model approximation, Commun.Math.Phys. 89 (1983) 191–220.
K. Gawedzki and A. Kupiainen: Continuum limit of the hierarchical non-linear O(N) sigma-model, Commun.Math. Phys. 106 (1986).
K.Gawedzki: The renormalization, from magic to mathematics, talk delivered at the International Congress of Mathematics (1986, Berkley).
Y. Higuchi and R. Lang: On the convergence of the Kadanoff transformation toward trivial fixed points, Z.Wahrscheinlichkeitstheorie verw.Gebiete, 58 (1981) 109–123.
K.R. Ito: Analytic study of the Migdal-Kadanoff recursion formlula, Commun.Math.Phys., 95 (1984) 247–255.
K.R. Ito: Permanent quark confinement in four-dimensional hierarchical lattice gauge theories of Migdal-Kadanoff type, Phys.Rev.Letters, 55 (1985) 558–562.
K.R.Ito: paper in preparation.
S.K. Ma: The modern theory of critical phenomena, Ch.8, (Benjamin, Massachusetts 1976).
V. Petrov: On the probabilities of large deviations for sums of independent random variables, Theory of Prob. and its Appl. 10 (1965) 287–298.
K. Wilson and J. Kogut: The renromalization group and ε-expansion, Phys.Rep. 12C (1974) 75–199.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Ito, K.R. (1988). Renormalization group method on a hierarchical lattice of dyson-wilson type. In: Watanabe, S., Prokhorov, J.V. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078469
Download citation
DOI: https://doi.org/10.1007/BFb0078469
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18814-8
Online ISBN: 978-3-540-48187-4
eBook Packages: Springer Book Archive