Abstract.
The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric ϕ4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summation in calculating the critical exponents, at the same time, yields the results that are in very good agreement with those of other rather complicated numerical methods. The principal advantage of the method of self-similar factor approximants is the combination of its extraordinary simplicity and high accuracy.
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References
H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University, New York, 1987)
V.I. Yukalov, A.S. Shumovsky, Lectures on Phase Transitions (World Scientific, Singapore, 1990)
D. Sornette, Critical Phenomena in Natural Sciences (Springer, Berlin, 2006)
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford Univeristy, Oxford, 1996)
V.I. Yukalov, Moscow Univ. Phys. Bull. 31, 10 (1976)
H. Kleinert, V. Schulte-Frohlinde, Critical Properties of ϕ4-Theories (World Scientific, Singapore, 2006)
H. Kleinert, Path Integrals (World Scientific, Singapore, 2006)
V.I. Yukalov, Phys. Rev. A 42, 3324 (1990)
V.I. Yukalov, Physica A 167, 833 (1990)
V.I. Yukalov, J. Math. Phys. 32, 1235 (1991)
V.I. Yukalov, J. Math. Phys. 33, 3994 (1992)
V.I. Yukalov, E.P. Yukalova, Physica A 225, 336 (1996)
V.I. Yukalov, S. Gluzman, Phys. Rev. Lett. 79, 333 (1997)
S. Gluzman, V.I. Yukalov, Phys. Rev. E 55, 3983 (1997)
V.I. Yukalov, E.P. Yukalova, Ann. Phys. 277, 219 (1999)
V.I. Yukalov, E.P. Yukalova, Chaos Solitons Fractals 14, 839 (2002)
H. Kleinert, V.I. Yukalov, Phys. Rev. E 71, 026131 (2005)
H.W. Blöte, A. Compagner, J.H. Croockewit, Y.T. Fonk, J.R. Heringa, A. Hoogland, T.S. Smit, A.L. van Villingen, Physica A 161, 1 (1989)
W. Janke, Phys. Lett. A 148, 306 (1990)
A.M. Ferrenberg, D.P. Landau, Phys. Rev. B 44, 5081 (1991)
C.F. Baillie, R. Gupta, K.A. Hawick, G.S. Pawley, Phys. Rev. B 45, 10438 (1992)
C. Holm, W. Janke, Phys. Lett. A 173, 8 (1993)
C. Holm, W. Janke, Phys. Rev. B 48, 936 (1993)
K. Chen, A.M. Ferrenberg, D.P. Landau, Phys. Rev. B 48, 3249 (1993)
C. Holm, W. Janke, J. Appl. Phys. 73, 5488 (1993)
B. Li, N. Madras, A.D. Sokal, J. Stat. Phys. 80, 661 (1995)
K. Kanaya, S. Kaya, Phys. Rev. D 51, 2404 (1995)
H.G. Ballesteros, L.A. Fernandez, V. Martin-Mayor, A.M. Sudupe, Phys. Lett. B 387, 125 (1996)
S. Caracciolo. M.S. Causo, A. Pelisseto, Phys. Rev. E 57, 1215 (1998)
V.I. Yukalov, S. Gluzman, D. Sornette, Physica A 328, 409 (2003)
S. Gluzman, V.I. Yukalov, D. Sornette, Phys. Rev. E 67, 026109 (2003)
V.I. Yukalov, S. Gluzman, Int. J. Mod. Phys. B 18, 3027 (2004)
V.I. Yukalov, E.P. Yukalova, Phys. Rev. A 72, 063611 (2005)
D.P. Landau, J. Magn. Magn. Mater. 200, 231 (1999)
M. Hasenbusch, J. Phys. A 34, 8221 (2001)
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. B 65, 144520 (2002)
Y. Deng, H.W. Blöte, Phys. Rev. E 68, 036125 (2003)
M. Hasenbusch, A. Pelissetto, E. Vicari, Phys. Rev. B 72, 014532 (2005)
M. Campostrini, M. Hasenbusch, A. Pelissetto, E. Vicari, Phys. Rev. B 74, 144506 (2006)
R. Guida, J. Zinn-Justin, J. Phys. A 31, 8103 (1998)
J. Zinn-Justin, Phys. Rep. 344, 159 (2001)
A. Pelissetto, E. Vicari, Phys. Rep. 368, 549 (2002)
R.N. Bhatt, A.P. Young, Phys. Rev. Lett. 54, 924 (1985)
A.T. Ogielski, I. Morgenstern, Phys. Rev. Lett. 54, 928 (1985)
A.T. Ogielski, Phys. Rev. B 32, 7384 (1985)
R.R.P. Singh, S. Chakravarty, Phys. Rev. B 36, 546 (1987)
R.R.P. Singh, S. Chakravarty, Phys. Rev. B 36, 559 (1987)
J.O. Andersen, Rev. Mod. Phys. 76, 599 (2004)
V.I. Yukalov, Laser Phys. Lett. 1, 435 (2004)
B. Kastening, Phys. Rev. A 68, 061601 (2003)
B. Kastening, Laser Phys. 14, 586 (2004)
B. Kastening, Phys. Rev. A 69, 043613 (2004)
J.L. Kneur, A. Neveu, M.B. Pinto, Phys. Rev. A 69, 053624 (2004)
B. Kastening, Phys. Rev. A 70, 043621 (2004)
J.L. Kneur, M.B. Pinto, Phys. Rev. A 71, 033613 (2005).
P. Arnold, G. Moore, Phys. Rev. Lett. 87, 120401 (2001)
V.A. Kashurnikov, N.V. Prokofiev, B.V. Svistunov, Phys. Rev. Lett. 87, 120402 (2001)
P. Arnold, G. Moore, Phys. Rev. E 64, 066113 (2001)
N.V. Prokofiev, B.V. Svistunov, Phys. Rev. Lett. 87, 160601 (2001)
K. Nho, D.P. Landau, Phys. Rev. A 70, 053614 (2004)
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Yukalov, V., Yukalova, E. Calculation of critical exponents by self-similar factor approximants. Eur. Phys. J. B 55, 93–99 (2007). https://doi.org/10.1140/epjb/e2007-00044-4
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DOI: https://doi.org/10.1140/epjb/e2007-00044-4