Abstract
We define a new model of interface roughening in one dimension which has the property that the minimum of interface height is conserved locally during the evolution. This model corresponds to the limit q → ∞ of the q-color dimer deposition-evaporation model introduced by us earlier [Hari Menon and Dhar, J. Phys. A: Math. Gen. 28:6517 (1995)]. We present numerical evidence from Monte Carlo simulations and the exact diagonalization of the evolution operator on finite rings that growth of correlations in this model is subdiffusive with dynamical exponent z≍2.5. For periodic boundary conditions, the variation of the gap in the relaxation spectrum with system size appears to involve a logarithmic correction term. Some generalizations of the model are briefly discussed.
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REFERENCES
A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge, 1995).
T. Halpin-Healy and Y. C. Zhang, Physics Reports 254:215 (1995).
M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56:889 (1986).
T. Sun, H. Gou, and M. Grant, Phys. Rev. A 40:6763 (1989).
Z. Rácz, M. Siegert, D. Liu, and M. Plischke, Phys. Rev. A 43:5275 (1991).
J. P. Doherty, M. A. Moore, J. M. Kim, and A. J. Bray, Phys. Rev. Lett. 72:2041 (1994).
M. Kardar and A. Zee, Nuclear Physics B 464:449 (1996).
M. Barma, M. D. Grynberg, and R. B. Stinchcombe, Phys. Rev. Lett. 70:1033 (1993).
D. Dhar and M. Barma, Pramana 41:L193 (1993).
M. Barma and D. Dhar, Phys. Rev. Lett. 73:2135 (1994).
M. Barma and D. Dhar, Proceedings of the International Colloquium on Modern Quantum Field Theory II, Bombay 1994 (World Scientific, Singapore).
P. B. Thomas, M. K. Hari Menon, and D. Dhar, J. Phys. A: Math. Gen. 27:L831 (1994).
M. K. Hari Menon and D. Dhar, J. Phys. A: Math. Gen. 28:6517 (1995).
G. I. Menon, M. Barma, and D. Dhar, J. Stat. Phys. 86:1237 (1997).
M. E. Cates and J. M. Deutsch, J. Phys. (Paris) 47:2121 (1986); M. Rubinstein, Phys. Rev. Lett. 57:3023 (1986); S. K. Nechaev, A. N. Semenov, and M. K. Koleva, Physica (Amsterdam) 140A:506 (1987).
S. P. Obukhov, M. Rubinstein, and T. Duke, Phys. Rev. Lett. 73:1263 (1994).
U. Alon and D. Mukamel, Phys. Rev. E 55:1783 (1997).
E. Brezin and S. R. Wadia, eds., The large N expansion in quantum field theory and statistical physics (World Scientific, Singapore, 1993).
P. E. Rouse, J. Chem. Phys. 48:1272 (1953).
H.-J. Ernst, F. Fabre, R. Folkerts, and J. Lapujoulade, Phys. Rev. Lett. 72:112 (1994); M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, J. Sudijono, L. M. Sander, and B. G. Orr, ibid, p. 116.
J. Krug and M. Schimschak, J. Phys. I France 5:1065 (1995).
J. M. Hammersley, in Proc. of V Berkeley Symposium on Math. Statistics and Probability, Vol. III, L. M. Le Cam and J. Neyman, eds. (Univ. California Press, Berkeley, 1967).
S. F. Edwards and D. R. Wilkinson, Proc. Roy. Soc. London A381:17 (1982).
F. C. Alcaraz, M. Droz, M. Henkel, and V. Rittenberg, Ann. Phys. 230:250 (1994).
W. Feller, An Introduction to Probability Theory and its Application (Wiley, 1968).
H. Hinrichsen, R. Livi, D. Mukamel, and A. Politi, Phys. Rev. Lett. 79:2710 (1997).
R. Lahiri and S. Ramaswamy, Phys. Rev. Lett. 79:1150 (1997).
M. R. Evans, Y. Kafri, H. M. Koduvely, and D. Mukamel, Cond-Mat 9707340.
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Koduvely, H.M., Dhar, D. A Model of Subdiffusive Interface Dynamics with a Local Conservation of Minimum Height. Journal of Statistical Physics 90, 57–77 (1998). https://doi.org/10.1023/A:1023291315658
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DOI: https://doi.org/10.1023/A:1023291315658