Abstract
We have simulated the two- and three-dimensional Ising models at their respective critical points with a conventional Monte Carlo algorithm. From the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz = 2.16–2.19 andz = 2.05, in agreement with the results quoted in the literature. We have also studied the power spectrum for the Kardar-Parisi-Zhang and Sun-Guo-Grant equations describing interface dynamics. Arguments similar to what was recently used to conclude thatz = 4 -η for model B in critical dynamics were applied to the Sun-Guo-Grant growth model and the known exact values for the roughening and dynamic exponents were obtained. From an analysis of the corresponding power spectrum in self-organized critical sand models one obtains a recently proposed hyperscaling relation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. McCoy and T. T. Wu,The Two-Dimensional Ising Model (Harvard University Press, Cambridge, Massachusetts, 1973).
P. C. Hohenberg and B. I. Halperin,Rev. Mod. Phys. 49:435 (1977).
S. Tang and D. P. Landau,Phys. Rev. B 36:567 (1987); S. Wansleben and D. P. Landau,Phys. Rev. B 43:6006 (1991).
D. Stauffer,Physica A 184:201 (1992); D. Stauffer,Int. J. Mod. Phys. C (1992).
P. H. Poole and N. Jan,J. Phys. A 23:L453 (1990).
K. MacIsaac and N. Jan,J. Phys. A 25:2139 (1992).
C. F. Baillie,Int. J. Mod. Phys. C 1:91 (1990).
K.-T. Leung,Phys. Rev. B 44:5340 (1991).
M. Suzuki,Prog. Theor. Phys. 58:1142 (1977); M. N. Barber, Finite-size scaling, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1983).
J. C. Angles d'Auriac, R. Maynard, and R. Rammal,J. Stat. Phys. 28:307 (1982).
O. F. de Alcantara Bonfin,Europhys. Lett. 4:373 (1987).
B. Schmittmann,Int. J. Mod. Phys. B 4:2269 (1990).
M. Kardar, G. Parisi, and Y.-C. Zhang,Phys. Rev. Lett. 56:889 (1986).
T. Sun, H. Guo, and M. Grant,Phys. Rev. A 40:6763 (1989).
P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. Lett. 59:381 (1987); P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. A 38:364 (1988).
K. Christensen, Z. Olami, and P. Bak,Phys. Rev. Lett. 68:2417 (1992).
D. Forster, D. R. Nelson, and M. J. Stephen,Phys. Rev. A 16:732 (1977).
T. Hwa and M. Kardar,Phys. Rev. Lett. 62:1813 (1989); T. Hwa and M. Kardar,Phys. Rev. A 45:7002 (1992).
D. E. Wolf and J. Villain,Europhys. Lett. 13:389 (1990).
Z.-W. Lai and S. Das Sarma,Phys. Rev. Lett. 66:2348 (1991).
F. Reif,Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), p. 585.
S.-K. Ma,Modern Theory of Critical Phenomena (Benjamin, 1976).
A. M. Ferrenberg and D. P. Landau,Phys. Rev. B 44:5081 (1991).
H. van Beijeren, R. Kutner, and H. Spohn,Phys. Rev. Lett. 54:2026 (1985); H. K. Janssen and B. Schmittmann,Z. Phys. B 63:517 (1986).
J. Krug,Phys. Rev. A 44:R801 (1991).
L. M. Sander and H. Yan,Phys. Rev. A 44:4885 (1991).
G. Grinstein, D.-H. Lee, and S. Sachdev,Phys. Rev. Lett. 64:1927 (1990).
H. G. E. Hentschel and F. Family,Phys. Rev. Lett. 66:1982 (1991).
P.-M. Lam and F. Family,Phys. Rev. A 44:7939 (1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lauritsen, K.B., Fogedby, H.C. Critical exponents from power spectra. J Stat Phys 72, 189–205 (1993). https://doi.org/10.1007/BF01048046
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01048046