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Prog. Theor. Phys. Vol. 64 No. 1 (1980) pp. 310-326

Critical Properties of Z(2) Lattice Gauge Systems from Strong-Coupling Expansions

Nobuyuki Kimura

Department of Physics, Hokkaido University, Sapporo 060

(Received March 1, 1980)

Abstract:

Phase transitions of Z(2) lattice gauge systems in D(=3 ∼5) dimnesional Euclidean space-time are investigated. We evaluate a string tension µ(x) to 14th order with respect to a natural expansion parameter x= tanh (1/g²) in confining phase. Through a few different analyses on the series, we estimate the value of critical coupling constants x_c within a few % error for D=4 and 5. D=4 result is consistent with two phase assumption. The series for D=3 does not have enough information to give a reliable estimation of x_c. Using Pade approximants, we examine two possible critical behaviors (i) µ(x) ∼(x_c² - x²)^γ and (ii) µ(x) ∼exp {- ρ(x_c²-x²)^{- δ} } of the string tension. As a reliability test of our method, we also perform similar analyses for a generalized model with different coupling constants for space and time directions.

URL : http://ptp.ipap.jp/link?PTP/64/310/
DOI : 10.1143/PTP.64.310

[ Full Text PDF : FREE ACCESS (1283K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. G. 't Hooft, Nucl. Phys. B 138 (1978), 1[CrossRef].
2. T. Yoneya, Nucl. Phys. B 144 (1978), 195[CrossRef].
   G. Mack and V. B. Petkova, Ann. of Phys. 123 (1979), 442[CrossRef].
3. R. Balian, J. M. Drouffe and C. Itzykson, Phys. Rev. D 10 (1974), 3376[APS]; ibid. 11 (1975), 2098[APS]; ibid. 11 (1975), 2104[APS].
4. E. Fradkin and L. Susskind, Phys. Rev. D 17 (1978), 2637[APS].
   J. M. Drouffe, Phys. Rev. D 18 (1978), 1174[APS].
   C. P. Korthals Altes, Nucl. Phys. B 142 (1978), 315[CrossRef].
   D. Horn, M. Weinstein and S. Yankielowicz, Phys. Rev. D 19 (1979), 3715[APS].
   S. Elitzur, R. B. Pearson and J. Shigemitsu, Phys. Rev. D 19 (1979), 3698[APS].
   A. Ukawa, P. Windy and A. H. Guth, Phys. Rev. D 21 (1980), 1013[APS].
   D. Boyanovsky, “Phases of Z(N) Lattice Gauge Theory” Centro Atómico Bariloche Preprint (1979).
   D. Boyanovsky and L. Masperi, “Variational Method for the Z(2) Gauge Model” Centro Atómico Bariloche Preprint (1979).
5. K. G. Wilson and J. B. Kogut, Phys. Rep. C 12 (1974), 76.
   J. B. Kogut, Rev. Mod. Phys. 51 (1979), 659[APS].
   T. Toneya, Soryushiron Kenkyu (Kyoto) 59-5 (1979), 229.
6. S. Elitzur, Phys. Rev. D 12 (1975), 3978[APS].
7. K. G. Wilson, Phys. Rev. D 10 (1974), 2445[APS].
8. K. G. Wilson, Erice Lecture in 1975, “New Phenomena in Subnuclear Physics”, A. Zichichi (eds.) (Plenum Press, New York, 1977); Phys. Rep. C 23 (1976), 331[CrossRef].
   L. Susskind, Les Houches Lecture in 1976, “Weak and Electromagnetic Interactions at High Energy”, R. Balian and C. H. L. Smith (eds.) (North-Holland Publishing Company, New York, 1977).
9. D. S. Gaunt and A. J. Guttman, in “Phase Transition and Critical Phenomena III”, C. Domb and M. Green (eds.) (Academic Press, New York, 1974).
10. G. A. Baker, Jr., in The Padé Approximant in Theoretical Physics, G. A. Baker, Jr. and J. L. Gammel (eds.) (Academic Press, New York, 1970).
11. J. M. Kosterlitz and D. J. Thouless, J. of Phys. C 6 (1973), 1181[IoP STACKS].
12. D. Horn and S. Yankielowicz, “Renormalization Group Calculation For Z(2) Gauge Theory”, Tel Aviv Univ. Preprint, TAUP 756-79.
13. A. A. Migdal, Sov.. Phys.-JETP 42 (1976), 413; ibid. 42 (1976), 743.
14. M. Creutz. L. Jacobs and C. Rebbi, Phys. Rev. Lett. 42 (1979), 1390[APS]; Phys. Rev. D 20 (1979), 1915[APS].
15. J. Cardy and H. Hamber, “Variational Calculations and the Nature of the Phase Transition in the Z(2) Gange Theory”, UCSB TH-33 (1979).

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