Prog. Theor. Phys. Vol. 50 No. 2 (1973) pp. 393-408

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On the Expansion Theory of Critical Exponents

— General Aspects and Some Applications —

Masuo Suzuki

Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo

(Received February 19, 1973)

Abstract:

General aspects of expansions of critical exponents are investigated with emphasis on matching conditions to determine them. There are given several suggestings and some applications to typical models of critical phenomena.

URL : http://ptp.ipap.jp/link?PTP/50/393/
DOI : 10.1143/PTP.50.393

References:

K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28 (1972), 240[APS].
M. E. Fisher and P. Pfeuty, Phys. Rev. B 6 (1972), 1889[APS].
F. Wegner, Phys. Rev. B 5 (1972), 4529[APS]; ibid. 6 (1972), 1891[APS].
K. G. Wilson, Phys. Rev. Lett. 28 (1972), 548[APS].
K. G. Wilson and J. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
E. Brezin, D. Wallace and K. Wilson, Phys. Rev. Lett. 29 (1972), 591[APS]; Phys. Rev. B 7 (1973), 232[APS].
M. E. Fisher, S. Ma and B. G. Nickel, Phys. Rev. Lett. 29 (1972), 917[APS].
M. Suzuki, Y. Yamazaki and G. Igarashi, Phys. Lett. A 42 (1972), 313[CrossRef].
E. K. Riedel and F. J. Wegner, Phys. Rev. Lett. 29 (1972), 349[APS].
F. J. Wegner and E. K. Riedel, Phys. Rev. B 7 (1973), 248[APS].
S. Ma, Phys. Rev. Lett. 29 (1972), 1311[APS]; Phys. Rev. A 6 (1973), 2172[APS].
R. Ferrell and D. Scalapino, Phys. Rev. Lett. 29 (1972), 413[APS].
R. Abe, Prog. Theor. Phys. 48 (1972), 1414[PTP]; ibid. 49 (1973), 113[PTP].
R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
S. Hikami, Prog. Theor. Phys. 49 (1973), 1096[PTP].
M. Suzuki, Phys. Lett. A 42 (1972), 5[CrossRef]; Prog. Theor. Phys. 49 (1973), 424[PTP]; ibid. 49 (1973), 1106[PTP]; ibid. 49 (1973), 1440[PTP]; ibid. 49 (1973), 1451[PTP].
T. Tsuneto and E. Abrahams, Phys. Rev. Lett. 30 (1973), 217[APS].
B. I. Halperin, P. C. Hohenberg and S. Ma, Phys. Rev. Lett. 29 (1972), 1548[APS].
M. Suzuki and G. Igarashi, Prog. Theor. Phys. 49 (1973), 1070[PTP].
K. G. Wilson, Phys. Rev. B 4 (1971), 3174[APS]; ibid. 4 (1971), 3184[APS].
C. Di Castro, Lett. Nuovo Cim. 5 (1972), 69.
T. Izuyama, a preprint.
R. J. Baxter, Phys. Rev. Lett. 26 (1971), 832[APS]; Ann. of Phys. 70 (1972), 193[CrossRef]; ibid. 70 (1972), 323[CrossRef].
L. Kadanoff and F. Wegner, Phys. Rev. B 4 (1971), 3989[APS].
F. Y. Wu, Phys. Rev. B 4 (1971), 2312[APS].
M. Suzuki, Phys. Rev. Lett. 28 (1972), 507[APS].
H. E. Stanley, Phys. Rev. 176 (1968), 718[APS].
L. P. Kadanoff, Proceedings of the Enrico Fermi Summer School, ed. by M. S. Green (Academic Press, 1972).
R. B. Griffiths, Phys. Rev. Lett. 24 (1970), 1479[APS].
R. Abe and S. Hikami, Phys. Lett. A 42 (1973), 419[CrossRef].
D. S. Greywall and G. Ahlers, Phys. Rev. Lett. 28 (1972), 1251[APS].
R. Abe, Prog. Theor. Phys. 49 (1973), 1074[PTP]; ibid. 49 (1973), 1877[PTP].
L. P. Kadanoff, Physics 2 (1966), 263.
B. Widom, J. Chem. Phys. 43 (1965), 3898[CrossRef].
C. Domb and D. L. Hunter, Proc. Phys. Soc. 86 (1965), 1147.
Z. A. Patashinsky and V. L. Pokrovsky, Sov. Phys. -JETP 50 (1966), 439.
C. Fan and F. Y. Wu, Phys. Rev. B 2 (1970), 723[APS].
L. Onsager, Phys. Rev. 65 (1944), 117[APS].
J. Sak, Phys. Rev. B 8 (1973), 281[APS].
G. S. Joyce, Phys. Rev. 146 (1966), 349[APS].
J. E. Nagle and J. C. Bonner, J. of Phys. C 3 (1970), 352[IoP STACKS].
M. Suzuki, Phys. Lett. A 43 (1973), 245[CrossRef].
H. Yahata and M. Suzuki, J. Phys. Soc. Jpn. 27 (1969), 1421[JPSJ].
H. Yahata, J. Phys. Soc. Jpn. 30 (1971), 657[JPSJ].
M. Suzuki, Intern. J. Magnetism 1 (1971), 123.
M. Suzuki, J. of Phys. C 7 (1974), 255[IoP STACKS].

Citing Article(s) :

Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 1085-1086 :
On the Critical Behavior of the Two-Dimensional Heisenberg-Ising Model

Masuo Suzuki and Fumihiko Tanaka
Progress of Theoretical Physics Vol. 52 No. 2 (1974) pp. 722-725 :
Perturbational Renormalization Group Approach to Critical Dynamics in Stochastic Models

Masuo Suzuki and Fumihiko Tanaka
Progress of Theoretical Physics Vol. 53 No. 1 (1975) pp. 97-110 :
On the Critical Dynamics in Bose Systems and the Time-Dependent Ginzburg-Landau Model

Masuo Suzuki
Progress of Theoretical Physics Vol. 54 No. 6 (1975) pp. 1679-1692 :
Coherent Representation of Dynamical Renormalization Group in Bose Systems

Fumihiko Tanaka
Progress of Theoretical Physics Vol. 54 No. 6 (1975) pp. 1693-1706 :
Study of Specific Heat below T_c in 1/n Expansion

Ryuzo Abe and Shinobu Hikami