Abstract
We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions d = 2 and 3, on square and simple cubic lattices. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (T f ) below the critical one (T c ), from different initial temperatures T i ≥ T c . In long time limit, for T i >T c , the persistence probability exhibits power-law decay with exponents θ ≃ 0.22 and ≃ 0.18 in d = 2 and 3, respectively. For finite T i , the early time behavior is a different power-law whose life-time diverges and exponent decreases as T i → T c . The two steps are connected via power-law as a function of domain length and the crossover to the second step occurs when this characteristic length exceeds the equilibrium correlation length at T = T i . T i = T c is expected to provide a new universality class for which we obtain θ ≡ θ c ≃ 0.035 in d = 2 and ≃0.105 in d = 3. The time dependence of the average domain size ℓ, however, is observed to be rather insensitive to the choice of T i .
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References
A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)
S. Puri, V. Wadhawan, Kinetics of Phase Transitions (Boca Raton, CRC Press, 2009)
A.J. Bray, Adv. Phys. 51, 481 (2002)
K. Binder, in Phase Transformation of Materials, edited by P. Haasen, Materials Science and Technology (VCH, Weinheim, 1991), Vol. 5, p. 405
M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)
T. Ohta, D. Jasnow, K. Kawasaki, Phys. Rev. Lett. 49, 1223 (1982)
A.J. Bray, S. Puri, Phys. Rev. Lett. 67, 2670 (1991)
H. Toyoki, Phys. Rev. B 45, 1965 (1992)
S.K. Das, S. Puri, M.C. Cross, Phys. Rev. E 64, 46206 (2001)
I.M. Lifshitz, V.V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961)
K. Binder, D. Stauffer, Phys. Rev. Lett. 33, 1006 (1974)
S.M. Allen, J.W. Cahn, Acta Metall. 27, 1085 (1979)
E.D. Siggia, Phys. Rev. A 20, 595 (1979)
D.A. Huse, Phys. Rev. B 34, 7845 (1986)
S. Majumder, S.K. Das, Phys. Rev. E 81, 050102 (2010)
S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev. Lett. 77, 2867 (1996)
S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996)
B. Derrida, V. Hakim, R. Zeitak, Phys. Rev. Lett. 77, 2871 (1996)
B. Derrida, Phys. Rev. E 55, 3705 (1997)
D. Stauffer, Int. J. Mod. Phys. C 8, 361 (1997)
G. Manoj, P. Ray, Phys. Rev. E 62, 7755 (2000)
D. Chakraborty, J.K. Bhattacharjee, Phys. Rev. E 76, 031117 (2007)
M. Saharay, P. Sen, Physica A 318, 243 (2003)
R. Paul, A. Gambassi, G. Schehr, Europhys. Lett. 78, 10007 (2007)
A.J. Bray, S.N. Majumdar, G. Schehr, Adv. Phys. 62, 225 (2013)
D.S. Fisher, D.A. Huse, Phys. Rev. B 38, 373 (1988)
F. Liu, G.F. Mazenko, Phys. Rev. B 44, 9185 (1991)
F. Corberi, E. Lippiello, M. Zannetti, Phys. Rev. E 74, 041106 (2006)
S. Ahmad, F. Corberi, S.K. Das, E. Lippiello, S. Puri, M. Zannetti, Phys. Rev. E 86, 061129 (2012)
S. Majumder, S.K. Das, Phys. Rev. Lett. 111, 055503 (2013)
J. Midya, S. Majumder, S.K. Das, J. Phys.: Condens. Matter 26, 452202 (2014)
C. Dasgupta, R. Pandit, Phys. Rev. B 33, 4752 (1986)
K. Humayun, A.J. Bray, J. Phys. A 24, 1915 (1991)
A.J. Bray, K. Humayun, T.J. Newman, Phys. Rev. B 43, 3699 (1991)
T. Blanchard, L.F. Cugliandolo, M. Picco, J. Stat. Mech. Theor. Exp. 2014, P12021 (2014)
A. Sicilia, J.A. Arenzon, A.J. Bray, L.F. Cugliandolo, Phys. Rev. E 76, 061116 (2007)
D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2009)
R.J. Glauber, J. Math. Phys. 4, 294 (1963)
M.E. Fisher, in Critical Phenomena, edited by M.S. Green (Academic Press, London, 1971)
S. Majumder, S.K. Das, Phys. Chem. Chem. Phys. 15, 13209 (2013)
Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, 1990)
S.K. Das, M.E. Fisher, J.V. Sengers, J. Horbach, K. Binder, Phys. Rev. Lett. 97, 25702 (2006)
S. Cueille, C. Sire, J. Phys. A 30, L791 (1997)
U. Wolff, Phys. Rev. Lett. 62, 361 (1989)
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Chakraborty, S., Das, S. Role of initial correlation in coarsening of a ferromagnet. Eur. Phys. J. B 88, 160 (2015). https://doi.org/10.1140/epjb/e2015-60168-4
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DOI: https://doi.org/10.1140/epjb/e2015-60168-4