Tunneling and the spectrum of the Potts model

Jing-Dong Wang; Carleton DeTar

doi:10.1103/PhysRevD.47.4091

Access by Xinjiang University

Tunneling and the spectrum of the Potts model

Jing-Dong Wang and Carleton DeTar

Department of Physics, University of Utah, Salt Lake City, Utah 84112

PDF

Phys. Rev. D 47, 4091 – Published 1 May, 1993

DOI: https://doi.org/10.1103/PhysRevD.47.4091

Abstract

The three-dimensional, three-state Potts model is studied as a paradigm for high-temperature quantum chromodynamics. In a high-statistics numerical simulation using a Swendson-Wang algorithm, we study cubic lattices of dimension as large as $64^{3}$ and measure correlation functions on long lattices of dimension $20^{2}$ × 120 and $30^{2}$ × 120. These correlations are controlled by the spectrum of the transfer matrix. This spectrum is studied in the vicinity of the phase transition. The analysis classifies the spectral levels according to an underlying $S_{3}$ symmetry. Near the phase transition the spectrum agrees nicely with a simple four-component Hamiltonian model. In the context of this model, we find that low-temperature ordered-ordered interfaces nearly always involve a disordered phase intermediate. We use a spectral method for determining the surface tension between phases.

References (17)

B. Svetitsky and L.G. Yaffe, Phys. Rev. D 26, 963 (1982) Nucl. Phys. B210, 423 (1982) J. Polónyi and K. Szlachányi, Phys. Lett. 100B, 395 (1982) T.A. DeGrand and C.E. DeTar, Nucl. Phys. B225 [FS9], 590 (1983) F. Green and F. Karsch, ibid. B238, 297 (1984) M. Okawa, Phys. Rev. Lett. 60, 1805 (1988)
J.P. Straley and M.E. Fisher, J. Phys. A 6, 1310 (1973) L. Susskind, Phys. Rev. D 20, 2610 (1979) S.J. Knak Jensen and O.G. Mouritsen, Phys. Rev. Lett. 43, 1736 (1979) F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982)
A. Ukawa, in Lattice '89, Proceedings of the International Symposium, Capri, Italy, 1989, edited by R. Petronzio [Nucl. Phys. B (Proc. Suppl.) 17, 118 (1990)]
APE Collaboration, P. Bacilieri et al., Phys. Rev. Lett. 61, 1545 (1988) Nucl. Phys. B318, 553 (1989)
F.R. Brown, N.H. Christ, Y. Deng, M. Gao, and T.J. Woch, Phys. Rev. Lett. 61, 2058 (1988)
R.V. Gavai, F. Karsch, and B. Petersson, Nucl. Phys. B322, 738 (1989) R.V. Gavai, S. Gupta, A. Irbäck, F. Karsch, and B. Petersson, ibid. B329, 263 (1990)
M. Fukugita, M. Okawa, and A. Ukawa, Phys. Rev. Lett. 63, 1768 (1989) Nucl. Phys. B337, 181 (1990) M. Fukugita and M. Okawa, Phys. Rev. Lett. 63, 13 (1989)
Jing-Dong Wang, Ph.D. thesis, University of Utah, 1992
K. Jansen, J. Jersak, I. Montvay, G. Münster, T. Trappenberg, and U. Wolff, Phys. Lett. B 213, 203 (1988)
R.H. Swendson and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987)
M.S. Challa, D.P. Landau, and K. Binder, Phys. Rev. B 34, 1841 (1986)
A.M. Ferrenberg and R.H. Swendson, Phys. Rev. Lett. 61, 2643 (1988)
F. Karsch and A. Patkós, Nucl. Phys. B350, 563 (1991)
K. Kajantie, L. Kärkkäinen, and K. Rummukainen, Nucl. Phys. B357, 693 (1991)
T. Trappenberg and U.J. Wiese, Nucl. Phys. B372, 703 (1992)
E. Brezin and J. Zinn-Justin, Nucl. Phys. B257, 867 (1985) V. Privman and M.E. Fisher, J. Stat. Phys. 33, 385 (1983)
B. Grossmann, M.L. Laursen, T. Trappenberg, and U.-J. Wiese, HLRZ Jülich Report No. 92-47, 1992 (unpublished)

[c1] B. Svetitsky and L.G. Yaffe, Phys. Rev. D 26, 963 (1982) Nucl. Phys. B210, 423 (1982) J. Polónyi and K. Szlachányi, Phys. Lett. 100B, 395 (1982) T.A. DeGrand and C.E. DeTar, Nucl. Phys. B225 [FS9], 590 (1983) F. Green and F. Karsch, ibid. B238, 297 (1984) M. Okawa, Phys. Rev. Lett. 60, 1805 (1988)

[c2] J.P. Straley and M.E. Fisher, J. Phys. A 6, 1310 (1973) L. Susskind, Phys. Rev. D 20, 2610 (1979) S.J. Knak Jensen and O.G. Mouritsen, Phys. Rev. Lett. 43, 1736 (1979) F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982)

[c3] A. Ukawa, in Lattice '89, Proceedings of the International Symposium, Capri, Italy, 1989, edited by R. Petronzio [Nucl. Phys. B (Proc. Suppl.) 17, 118 (1990)]

[c4] APE Collaboration, P. Bacilieri et al., Phys. Rev. Lett. 61, 1545 (1988) Nucl. Phys. B318, 553 (1989)

[c5] F.R. Brown, N.H. Christ, Y. Deng, M. Gao, and T.J. Woch, Phys. Rev. Lett. 61, 2058 (1988)

[c6] R.V. Gavai, F. Karsch, and B. Petersson, Nucl. Phys. B322, 738 (1989) R.V. Gavai, S. Gupta, A. Irbäck, F. Karsch, and B. Petersson, ibid. B329, 263 (1990)

[c7] M. Fukugita, M. Okawa, and A. Ukawa, Phys. Rev. Lett. 63, 1768 (1989) Nucl. Phys. B337, 181 (1990) M. Fukugita and M. Okawa, Phys. Rev. Lett. 63, 13 (1989)

[c8] Jing-Dong Wang, Ph.D. thesis, University of Utah, 1992

[c9] K. Jansen, J. Jersak, I. Montvay, G. Münster, T. Trappenberg, and U. Wolff, Phys. Lett. B 213, 203 (1988)

[c10] R.H. Swendson and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987)

[c11] M.S. Challa, D.P. Landau, and K. Binder, Phys. Rev. B 34, 1841 (1986)

[c12] A.M. Ferrenberg and R.H. Swendson, Phys. Rev. Lett. 61, 2643 (1988)

[c13] F. Karsch and A. Patkós, Nucl. Phys. B350, 563 (1991)

[c14] K. Kajantie, L. Kärkkäinen, and K. Rummukainen, Nucl. Phys. B357, 693 (1991)

[c15] T. Trappenberg and U.J. Wiese, Nucl. Phys. B372, 703 (1992)

[c16] E. Brezin and J. Zinn-Justin, Nucl. Phys. B257, 867 (1985) V. Privman and M.E. Fisher, J. Stat. Phys. 33, 385 (1983)

[c17] B. Grossmann, M.L. Laursen, T. Trappenberg, and U.-J. Wiese, HLRZ Jülich Report No. 92-47, 1992 (unpublished)

Physical Review D

Export citation

Export citation

Tunneling and the spectrum of the Potts model

Abstract

References (17)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation