Abstract
We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a φ3 critical dynamics model describing universal properties of metastable states in the vicinity of a firstorder phase transition and a reaction-diffusion system near the point of a second-order transition between fluctuation and absorption states (a simple epidemic process or the Gribov process). In both cases, we demonstrate the existence of a new strongly nonequilibrium, anisotropic scaling regime (universality class) for which both the mixing and the nonlinearity in the order parameter are relevant. We evaluate the corresponding critical dimensions in the one-loop approximation of the renormalization group.
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References
A. N. Vasil’ev, Quantum Field Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], Izd. PIYaF, St. Petersburg (1998); English transl.: The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics, Chapman and Hall/CRC, Boca Raton, Fla. (2004).
H.-K. Janssen and U. C. Täuber, Ann. Phys., 315, 147–192 (2004); arXiv:cond-mat/0409670v1 (2004).
D. Yu. Ivanov, Critical Behavior of Nonidealized Systems [in Russian], Fizmatlit, Moscow (2003).
A. Onuki and K. Kawasaki, Progr. Theoret. Phys., 63, 122–139 (1980); T. Imaeda, A. Onuki, and K. Kawasaki, Progr. Theoret. Phys., 71, 16–26 (1984).
D. Beysens, M. Gbadamassi, and L. Boyer, Phys. Rev. Lett., 43, 1253–1256 (1979); D. Beysens and M. Gbadamassi, J. Phys. Lett., 40, 565–567 (1979).
R. Ruiz and D. R. Nelson, Phys. Rev. A, 23, 3224–3246 (1981); 24, 2727–2734 (1981); J. A. Aronowitz and D. R. Nelson, Phys. Rev. A, 29, 2012–2016 (1984).
N. V. Antonov, M. Hnatich, and J. Honkonen, J. Phys. A, 39, 7867–7887 (2006); arXiv:cond-mat/0604434v1 (2006).
N. V. Antonov and A. A. Ignatieva, J. Phys. A, 39, 13593–13620 (2006); arXiv:cond-mat/0607019v1 (2006); N. V. Antonov, A. A. Ignatieva, and A. V. Malyshev, Phys. Part. Nucl., 41, 998–1000 (2010); arXiv:1003.2855v1 [cond-mat.stat-mech] (2010).
N. V. Antonov, V. I. Iglovikov, and A. S. Kapustin, J. Phys. A, 42, 135001 (2009); arXiv:0808.0076v1 [condmat. stat-mech] (2008); N. V. Antonov and A. S. Kapustin, J. Phys. A, 43, 405001 (2010); arXiv:1006.3133v1 [cond-mat.stat-mech] (2010).
F. Zhong and Q. Chen, Phys. Rev. Lett., 95, 175701 (2005).
M. Avellaneda and A. J. Majda, Comm. Math. Phys., 131, 381–429 (1990); 146, 139–204 (1992).
G. Falkovich, K. Gawędzki, and M. Vergassola, Rev. Modern Phys., 73, 913–975 (2001); arXiv:cond-mat/ 0105199v1 (2001).
N. V. Antonov, J. Phys. A, 39, 7825–7865 (2006).
M. E. Fisher, Phys. Rev. Lett., 40, 1610–1613 (1978).
C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett., 93, 251601 (2004); arXiv:hep-th/0402011v3 (2004).
O. F. de Alcantara Bonfim, J. E. Kirkham, and A. J. McKane, J. Phys. A, 13, L247–L251 (1980); 14, 2391–2413 (1981).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 1, pp. 50–77, April, 2011.
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Antonov, N.V., Malyshev, A.V. The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems. Theor Math Phys 167, 444–467 (2011). https://doi.org/10.1007/s11232-011-0034-x
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DOI: https://doi.org/10.1007/s11232-011-0034-x