Abstract
An effective free energy for a fluctuating system is investigated using an exact (local) renormalization group (RG) equation. This equation accounts for the fluctuation interaction in a reduced manner (at Fisher exponent η=0) and leads to a physical solution branch which gives realistic estimations for the free energy and nice critical exponents. It is shown that in spite of the monotonic character of the effective free energy in the critical region, all vertices should be taken into account in the effective Ginzburg-Landau-Wilson functional. The large-scale structure of the fluctuating field at a second-order phase transition is studied utilizing the calculated free energy and localized nonlinear excitations are found with profiles rather like those previously obtained in a model approach.
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References
L. D. Landau and E. M. Lifshits,Statistical Physics, 3rd ed. (Nauka, Moscow, 1976).
L. D. Landau and L. P. Pitayevsky,Physical Kinetics (Nauka, Moscow, 1976).
L. D. Landau and I. M. Khalatnikov, inL. D. Landau Collected Work (Nauka, Moscow, 1969, Vol. 2, pp. 218–222.
J. A. Tuszynski, R. Paul, and R. Catterjee,Phys. Rev. B 29:380 (1984).
J. A. Tuszynski, M. Otwinowski, R. Paul, and A. P. Smith,Phys. Rev. B 36:2190 (1987).
J. A. Tuszynski, M. Otminowski, R. Paul, and A. P. Smith,Phys. Rev. B 36:2190 (1987).
J. A. Tuszynski and R. Paul,Phys. Rev. B 29:380 (1984).
A. E. Filippov, Yu. E. Kuzovlev, and T. K. Soboleva,Phys. Lett. A 165:159 (1992);178:301 (1993).
Yu. E. Kuzovlev, T. K. Soboleva, and A. E. Filippov,Sov. Phys. JETP 103:858 (1993).
Yu. E. Kuzovlev, T. K. Soboleva, and A. E. Filippov,JETP Lett. 58(5) (1993).
K. G. Wilson,Phys. Rev. B 4:3174 (1971).
K. G. Wilson and M. E. Fisher,Phys. Rev. Lett. 28:240 (1972).
K. G. Wilson and G. Kogut,Phys. Rep. 12C:240 (1974).
A. Aharony, inPhase Transitions and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (Academic Press, New York, 1976), p. 357.
A. Z. Patashinskii and V. L. Pokrovskii,Fluktuatsionnaya Teoriya Kriticheskikh Yavlenii (Mir, Moscow, 1982).
D. M. Mukamel and S. Krinsky,Phys. Rev. B 13:5065 (1976).
D. M. Mukamel and S. Krinsky,J. Phys. C 8:L496 (1975).
Yu. M. Ivanchenko, A. E. Filippov, and A. V. Radievsky,Fiz. Nizk. Temp. (Sov. Low Temp. Phys.) 18:957 (1992).
Yu. M. Ivanchenko, A. E. Filippov, and A. V. Radievsky,J. Stat. Phys. 71:1001 (1992).
T. Schneider, E. Stoll, and H. Beck,Physica A 79:201 (1975).
E. K. Riedel, G. R. Golner, and K. E. Newman,Ann. Phys. (NY)161:178 (1985).
G. R. Golner,Phys. Rev. B 33:7863 (1986).
A. Hasenfratz and P. Hasenfratz,Nucl. Phys. B 270:687 (1986).
G. Felder,Commun. Math. Phys. 11:101 (1987).
P. Shukla and M. S. Green,Phys. Rev. Lett. 34:436 (1975).
G. R. Golner and E. K. Riedel,Phys. Rev. Lett. 34:171 (1975).
V. I. Tokar,Phys. Lett. A 104:135 (1984).
Yu. M. Ivanchenko, A. A. Lisyanskii, and A. E. Filippov,J. Stat. Phys. 58:295 (1990).
Yu. M. Ivanchenko, A. A. Lisyanskii, and A. E. Filippov,J. Stat. Phys. 66:1667 (1992).
A. E. Filippov and S. A. Breus,Phys. Lett. A 158:300 (1991).
S. A. Breus and A. E. Filippov,Physica A 192:480 (1993).
A. E. Filippov and A. V. Radievsky,Sov, Phys. JETP 102:1022 (1992).
S.-K. Ma,Modern Theory of Critical Phenomena (Benjamin, 1976).
Q. Zang and J. P. Badiali,Phys. Rev. Lett. 67:1598 (1991).
Q. Zang and J. P. Badiali,Phys. Rev. A 45:8666 (1991).
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Filippov, A.E. Large-scale structure of fluctuating order parameter field. J Stat Phys 75, 241–252 (1994). https://doi.org/10.1007/BF02186288
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DOI: https://doi.org/10.1007/BF02186288