Abstract
A review of bond-moving and variational approximation methods in real-space renormalization is presented. Some of the more important developments in this field are illustrated in detail, using the Ising model as an example. Particular emphasis is placed on the Migdal-Kadanoff transformation and the Kadanoff lower-bound variational transformation. The successes and inherent limitations of the bond-moving and variational approximations are discussed. References to various applications of the methods are given.
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
Th. Niemeijer, J.M.J. van Leeuwen: In Phase Transitions and Critical Phenomena, Vol.6, ed. by C. Domb, M.S. Green ( Academic, New York 1976 )
L.P. Kadanoff: Phys. Rev. Lett. 34, 1005 (1975)
L.P. Kadanoff, A. Houghton, M.C. Yalabik: J. Stat. Phys. 14, 171 (1976)
W. van Saarloos, J.M.J. van Leeuwen, A.M.M. Pruisken: Physica 92A, 323 (1978)
M.P.M. den Nijs, H.J.F. Knops: Physica 93A, 441 (1978)
M.N. Barber: J. Phys. A10, 1721 (1977)
M. Droz, S.L. Katz, J.D. Gunton: Phys. Rev. B15, 237 (1977)
M. Kohmoto, L.P. Kadanoff: J. Phys. A13, 3339 (1980)
M.C. Yalabik, A. Houghton: Phys. Lett. 61A, 1 (1977)
T.W. Burkhardt: Phys. Rev. B14, 1196 (1976)
T.W. Burkhardt, H.J.F. Knops: Phys. Rev. B15, 1602 (1977)
C. Dasgupta: Phys. Rev. B14, 1221 (1976); Phys. Rev. B15, 3460 (1977)
T.W. Burkhardt, H.J.F. Knops, M. den Nijs: J. Phys. A9, L179 (1976)
M.P.M. den Nijs: Physica 95A, 449 (1979)
S.E. Ashley, M.B. Green: J. Phys. A9, L165 (1976)
S.E. Ashley: J. Phys. All, 2015 (1978)
B. Nienhuis, E.K. Riedel, M. Schick: J. Phys. A13, L31, L189 (1980); Phys. Rev. B23, 6055 (1981)
T.W. Burkhardt: Z. Phys. B39, 159 (1980)
H.J.F. Knops: Physica 93A, 427 (1978)
M. Droz, A. Malaspinas: J. Phys. C11, 2729 (1978)
V.R. Vieira, J.A. Hertz: Phys. Rev. B21, 2336 (1980)
S.L. Katz, J.D. Gunton: Phys. Rev. 816, 2163 (1977)
Y.M. Shih, D.C. Jou, C.K. Pan, W.S. Lee, W.D. Chen, H.M. Huang, C.K. Hu, K.G. Chen, H.C. Tseng: Phys. Rev. 819, 529 (1979)
Y.M. Shih, D.C. Jou, C.K. Pan, W.D. Chen, H.M. Huang, C.K. Hu, K.G. Chen, W.S. Lee, D.S. Wan, H.C. Tseng: Phys. Rev. B21, 299 (1980)
S.L. Katz, M. Droz, J.D. Gunton: Phys. Rev. B15, 1597 (1977)
N. Jan, A.M. Glazer: Physica 91A, 461 (1978)
B.W. Southern: J. Phys. All, Li (1978)
B. Schuh: Z. Phys. B31, 55 (1978)
M.J. de Oliveira, D. Furman, R.B. Griffiths: Phys. Rev. Lett. 40, 977 (1978)
T.W. Burkhardt, E. Eisenriegler: Phys. Rev. B17, 318 (1978)
T.W. Burkhardt, R.H. Swendsen: Phys. Rev. B13, 3071 (1976)
T.W. Burkhardt, W. Kinzel: Phys. Rev. B20, 4730 (1979)
A.A. Migdal: Sov. Phys. JETP 42, 743 (1976)
A.A. Migdal: Sov. Phys. JETP 42, 413 (1976)
L.P. Kadanoff: Ann. Phys. (N.Y.) 100, 359 (1976)
M.N. Barber: J. Phys. A10, 1187 (1977)
S.J. Shenker, L.P. Kadanoff, A.M.M. Pruisken: J. Phys. Al2, 91 (1979)
L.P. Kadanoff, A. Houghton: Phys. Rev. B11, 377 (1975)
D.J. Wallace, R.K.P. Zia: Phys. Rev. Lett. 43, 808 (1979)
D. Forster, A. Gabriunas: Phys. Rev. A23, 2627 (1981); A24, 598 (1981)
A.M. Polyakov: Phys. Lett. 59B, 79 (1975)
E. Brézin, J. Zinn-Justin: Phys. Rev. Lett. 36, 691 (1976); Phys. Rev. B14, 3110 (1976)
R. Lipowsky, H. Wagner: Z. Phys. 42, 355 (1981)
B. Nienhuis, M. Nauenberg: Phys. Rev. Lett. 35, 477 (1975)
M. Blume, V.J. Emery, R.B. Griffiths: Phys. Rev. A4, 1071 (1971)
V.J. Emery, R.H. Swendsen: Phys. Lett. 64A, 325 (1977)
M. Kaufman, R.B. Griffiths, J.M. Yeomans, M.E. Fisher: Phys. Rev. B23, 3448 (1981)
D. Andelman, A.N. Berker: J. Phys. A14, L91 (1981)
G. Forgâcs, A. Zawadowski: Unpublished
A.N. Berker, S. Ostlund: J. Phys. C12, 4961 (1979)
M. Kaufman, R.B. Griffiths: Phys. Rev. B24, 496 (1981)
J.V. José, L.P. Kadanoff, S. Kirkpatrick, D.R. Nelson: Phys. Rev. B16, 1217 (1977)
J.L. Cardy, D.J. Scalapino: Phys. Rev. B19, 1428 (1979)
A.N. Berker, D.R. Nelson: Phys. Rev. B19, 2488 (1979)
V.J. Emery, R.H. Swendsen: Phys. Rev. Lett. 39, 1414 (1977)
E. Domany, E.K. Riedel: Phys. Rev. Lett. 40, 561 (1978); Phys. Rev. B19, 5817 (1979)
A.N. Berker, S. Ostlund, F.A. Putnam: Phys. Rev. B17, 3650 (1978)
S. Ostlund, A.N. Berker: Phys. Rev. Lett. 42, 843 (1979)
R.M. Hornreich, R. Liebmann, H.G. Schuster, W. Selke: Z. Phys. B35, 91 (1979)
B.W. Southern, A.P. Young: J. Phys. C10, 2179 (1977)
B.W. Southern, A.P. Young, P. Pfeuty: J. Phys. C12, 683 (1979)
S. Kirkpatrick: Phys. Rev. B15, 1533 (1977)
C. Jayaprakash, J. Chalupa, M. Wortis: Phys. Rev. B15, 1495 (1977)
C. Jayaprakash, E.K. Riedel, M. Wortis: Phys. Rev. B18, 2244 (1978)
Y. Gefen, B.B. Mandelbrot, A. Aharony: Phys. Rev. Lett. 45, 855 (1980)
M. Suzuki, K. Sogo, I. Matsuba, H. Ikeda, T. Chikama, H. Takano: Prog. Theor. Phys. 61, 864 (1979)
M. Droz: Phys. Lett. 73A, 407 (1979)
J.0. Indekeu, A. Stella: Phys. Lett. 78A, 160 (1980)
M. Suzuki, H. Takano: Phys. Lett. 69A, 426 (1979)
M. Barma, D. Kumar, R.B. Pandey: J. Phys. C12, L909 (1979)
C. Castellani, C. Di Castro, J. Ranninger: Nucl. Phys. B200, 45 (1982)
S. Caracciolo, P. Menotti: Nucl. Phys. B, to be published
M. Nauenberg, D. Toussaint: Nucl. Phys. B190, 217 (1981)
T.W. Burkhardt, B.W. Southern: J. Stat. Phys. 20, 247 (1979)
T.W. Burkhardt: Phys. Rev. B20, 2905 (1979)
L.S. Lucena, W. Klein, R.K.P. Zia: To be published
G. Martinelli, G. Parisi: Nucl. Phys. B180, 201 (1981)
G. Martinelli, P. Menotti: Nucl. Phys. B, to be published
T.W. Burkhardt: Phys. Rev. B13, 3187 (1976)
L.P. Kadanoff: J. Stat. Phys. 15, 263 (1976)
J.C. Le Guillou, J. Zinn-Justin: Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B21, 3976 (1980)
B. Nienhuis, A.N. Berker, E.K. Riedel, M. Schick: Phys. Rev. Lett. 43, 737 (1979)
J.L. Black, V.J. Emery: Phys. Rev. B23, 429 (1981)
R.B. Pearson: Phys. Rev. B22, 2579 (1980)
H.J.F. Knops: Physica 86A, 448 (1977)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Burkhardt, T.W. (1982). Bond-Moving and Variational Methods in Real-Space Renormalization. In: Burkhardt, T.W., van Leeuwen, J.M.J. (eds) Real-Space Renormalization. Topics in Current Physics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81825-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-81825-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81827-1
Online ISBN: 978-3-642-81825-7
eBook Packages: Springer Book Archive