Dynamic scaling in diluted systems: Deactivation through thermal dilution

Manuel I. Marqués; Julio A. Gonzalo

doi:10.1103/PhysRevE.63.056114

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Dynamic scaling in diluted systems: Deactivation through thermal dilution

Manuel I. Marqués and Julio A. Gonzalo^*

Departamento de Física de Materiales C-IV, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain

^*Email address: julio.gonzalo@uam.es

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Phys. Rev. E 63, 056114 – Published 18 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.056114

Abstract

Activated scaling is confirmed to hold in transverse field-induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold ${(p}_{c})$ but also well below and above it. We follow the evolution of the activated scaling at zero temperature in the phase transition from ferromagnetic to quantum Griffiths phase $(p > p_{c})$ at the phase boundary ${(p = p}_{c})$ and for transitions inside the nonferromagnetic quantum Griffiths phase $(p < p_{c}) .$ A novel deactivation phenomenon inside the nonferromagnetic Griffiths-McCoy phase $(p < p_{c})$ is observed using a thermal (in contrast to random) dilution of the system.

References (36)

R.B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).
B.M. McCoy, Phys. Rev. Lett. 23, 383 (1969); Phys. Rev. 188, 1014 (1969).
D.S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).
R. Shankar and G. Murthy, Phys. Rev. B 36, 536 (1987).
B.M. McCoy and T.T. Wu, Phys. Rev. 176, 631 (1968); ibid.188, 982 (1969).
R.H. McKenzie, Phys. Rev. Lett. 77, 4804 (1996).
F. Iglói and H. Rieger, Phys. Rev. B 57, 11 404 (1998).
A.P. Young, Phys. Rev. B 56, 11 691 (1997).
W. Wu, D. Bitko, T.F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 71, 1919 (1993).
A.H. Castro Neto, G. Castilla, and B.A. Jones, Phys. Rev. Lett. 81, 3531 (1998).
M.C. de Andrade, R. Chau, R.P. Dickey, N.R. Dilley, E.J. Freeman, D.A. Gajewski, M.B. Maple, R. Movshovich, A.H. Castro Neto, G. Castilla, and B.A. Jones, Phys. Rev. Lett. 81, 5620 (1998).
H. Rieger and F. Iglói, Phys. Rev. Lett. 83, 3741 (1999).
H. Rieger and A.P. Young, Phys. Rev. Lett. 72, 4141 (1994).
M. Guo, R.N. Bhatt, and D.A. Huse, Phys. Rev. Lett. 72, 4137 (1994).
C. Pich, A.P. Young, H. Rieger, and N. Kawashima, Phys. Rev. Lett. 81, 5916 (1998).
H. Rieger and N. Kawashima, Eur. Phys. J. B 9, 233 (1999).
O. Motrunich, S. -C. Mau, D.A. Huse, and D.S. Fisher, Phys. Rev. B 61, 1160 (2000).
T. Senthil and S. Sachdev, Phys. Rev. Lett. 77, 5292 (1996).
A.B. Harris, J. Phys. C 7, 3082 (1974).
R.B. Stinchcombe, J. Phys. C 14, L263 (1981).
S. Bhattacharya and P. Ray, Phys. Lett. 101A, 346 (1984).
T. Ikegami, S. Miyashita, and H. Rieger, J. Phys. Soc. Jpn. 67, 2761 (1998).
M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976); in Quantum Monte Carlo Methods, edited by M. Suzuki (Springer-Verlag, Heidelberg, 1987), p. 1.
U. Wolff, Phys. Rev. Lett. 62, 361 (1989).
A. Weinrib and B.I. Halperin, Phys. Rev. B 27, 413 (1983).
A. Aharony, A.B. Harris, and S. Wiseman, Phys. Rev. Lett. 81, 252 (1998).
R.M. Ziff, Phys. Rev. Lett. 69, 2670 (1992).
A.P. Young and H. Rieger, Phys. Rev. B 53, 8486 (1996).
F. Iglói and H. Rieger, Phys. Rev. Lett. 78, 2473 (1997).
H. Rieger and F. Iglói, Europhys. Lett. 39, 135 (1997).
M.J. Thill and D.A. Huse, Physica 214A, 321 (1995).
H. Rieger and A.P. Young, Phys. Rev. B 54, 3328 (1996).
M. Guo, R.N. Bhatt, and D.A. Huse, Phys. Rev. B 54, 3336 (1996).
M.I. Marqués and J.A. Gonzalo, Phys. Rev. E 60, 2394 (1999).
M.I. Marqués, J.A. Gonzalo, and J. Íñiguez, Phys. Rev. E 62, 191 (2000).
S. Prakash, S. Havlin, M. Schwartz, and H.E. Stanley, Phys. Rev. A 46, R1724 (1992).

[c1] R.B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).

[c2] B.M. McCoy, Phys. Rev. Lett. 23, 383 (1969); Phys. Rev. 188, 1014 (1969).

[c3] D.S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).

[c4] R. Shankar and G. Murthy, Phys. Rev. B 36, 536 (1987).

[c5] B.M. McCoy and T.T. Wu, Phys. Rev. 176, 631 (1968); ibid.188, 982 (1969).

[c6] R.H. McKenzie, Phys. Rev. Lett. 77, 4804 (1996).

[c7] F. Iglói and H. Rieger, Phys. Rev. B 57, 11 404 (1998).

[c8] A.P. Young, Phys. Rev. B 56, 11 691 (1997).

[c9] W. Wu, D. Bitko, T.F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 71, 1919 (1993).

[c10] A.H. Castro Neto, G. Castilla, and B.A. Jones, Phys. Rev. Lett. 81, 3531 (1998).

[c11] M.C. de Andrade, R. Chau, R.P. Dickey, N.R. Dilley, E.J. Freeman, D.A. Gajewski, M.B. Maple, R. Movshovich, A.H. Castro Neto, G. Castilla, and B.A. Jones, Phys. Rev. Lett. 81, 5620 (1998).

[c12] H. Rieger and F. Iglói, Phys. Rev. Lett. 83, 3741 (1999).

[c13] H. Rieger and A.P. Young, Phys. Rev. Lett. 72, 4141 (1994).

[c14] M. Guo, R.N. Bhatt, and D.A. Huse, Phys. Rev. Lett. 72, 4137 (1994).

[c15] C. Pich, A.P. Young, H. Rieger, and N. Kawashima, Phys. Rev. Lett. 81, 5916 (1998).

[c16] H. Rieger and N. Kawashima, Eur. Phys. J. B 9, 233 (1999).

[c17] O. Motrunich, S. -C. Mau, D.A. Huse, and D.S. Fisher, Phys. Rev. B 61, 1160 (2000).

[c18] T. Senthil and S. Sachdev, Phys. Rev. Lett. 77, 5292 (1996).

[c19] A.B. Harris, J. Phys. C 7, 3082 (1974).

[c20] R.B. Stinchcombe, J. Phys. C 14, L263 (1981).

[c21] S. Bhattacharya and P. Ray, Phys. Lett. 101A, 346 (1984).

[c22] T. Ikegami, S. Miyashita, and H. Rieger, J. Phys. Soc. Jpn. 67, 2761 (1998).

[c23] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976); in Quantum Monte Carlo Methods, edited by M. Suzuki (Springer-Verlag, Heidelberg, 1987), p. 1.

[c24] U. Wolff, Phys. Rev. Lett. 62, 361 (1989).

[c25] A. Weinrib and B.I. Halperin, Phys. Rev. B 27, 413 (1983).

[c26] A. Aharony, A.B. Harris, and S. Wiseman, Phys. Rev. Lett. 81, 252 (1998).

[c27] R.M. Ziff, Phys. Rev. Lett. 69, 2670 (1992).

[c28] A.P. Young and H. Rieger, Phys. Rev. B 53, 8486 (1996).

[c29] F. Iglói and H. Rieger, Phys. Rev. Lett. 78, 2473 (1997).

[c30] H. Rieger and F. Iglói, Europhys. Lett. 39, 135 (1997).

[c31] M.J. Thill and D.A. Huse, Physica 214A, 321 (1995).

[c32] H. Rieger and A.P. Young, Phys. Rev. B 54, 3328 (1996).

[c33] M. Guo, R.N. Bhatt, and D.A. Huse, Phys. Rev. B 54, 3336 (1996).

[c34] M.I. Marqués and J.A. Gonzalo, Phys. Rev. E 60, 2394 (1999).

[c35] M.I. Marqués, J.A. Gonzalo, and J. Íñiguez, Phys. Rev. E 62, 191 (2000).

[c36] S. Prakash, S. Havlin, M. Schwartz, and H.E. Stanley, Phys. Rev. A 46, R1724 (1992).

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Dynamic scaling in diluted systems: Deactivation through thermal dilution

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