Phase transitions of the binary production <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mrow><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow></mrow><mn>3</mn><mi>A</mi><mo>,</mo><mi></mi><mn>4</mn><mrow><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow></mrow><mi>∅</mi></math></span> model

Géza Ódor

doi:10.1103/PhysRevE.69.036112

Access by Xinjiang University

Phase transitions of the binary production $2 \vec{A} 3 A, 4 \vec{A} \emptyset$ model

Géza Ódor

Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary

PDF

Phys. Rev. E 69, 036112 – Published 23 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.036112

Abstract

Phase transitions of the $2 \vec{A} 3 A,$ $4 \vec{A} \emptyset$ reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations. The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the site mean-field approximation shows a single transition at zero branching rate introduced by Ódor [G. Ódor, Phys. Rev. E 67, 056114 (2003)], $N > 2$ cluster approximations predict the appearance of another transition line for weak diffusion (D) as well. The latter phase transition is continuous, occurs at finite branching rate, and exhibits different scaling behavior. I show that the universal behavior of these transitions is in agreement with that of the difffusive pair contact process model both on the mean-field level and in one dimension. Therefore this model exhibiting annihilation by quadruplets does not fit in the recently suggested classification of universality classes of absorbing state transitions in one dimension [J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003)]. For high diffusion rates the effective $2 \vec{A} 3 \vec{A} 4 \vec{A} \emptyset$ reaction becomes irrelevant and the model exhibits a mean-field transition only. The two regions are separated by a nontrivial critical end point at $D^{*} .$

References (38)

For references see J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
H. Berry, Phys. Rev. E 67, 031907 (2003).
J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
H. Hinrichsen, Adv. Phys. 49, 815 (2000).
G. Ódor, Rev. Mod. Phys (to be published), e-print cond-mat/0205644.
U. Täuber, Adv. Solid State Phys. 43, 659 (2003).
P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982).
E. Carlon, M. Henkel, and U. Schollwöck, Phys. Rev. E 63, 036101 (2001).
H. Hinrichsen, Phys. Rev. E 63, 036102 (2001).
G. Ódor, Phys. Rev. E 62, R3027 (2000).
H. Hinrichsen, Physica A 291, 275 (2001).
G. Ódor, Phys. Rev. E 63, 067104 (2001).
J.D. Noh and H. Park, Phys. Rev. E 69, 016122 (2004).
M. Henkel and U. Schollwöck, J. Phys. A 34, 3333 (2001).
M. Henkel and H. Hinrichsen, J. Phys. A 34, 1561 (2001).
K. Park, H. Hinrichsen, and In-mook Kim, Phys. Rev. E 63, 065103(R) (2001).
G. Ódor, M.A. Santos, and M.C. Marques, Phys. Rev. E 65, 056113 (2002).
G. Ódor, Phys. Rev. E 65, 026121 (2002).
K. Park and I. Kim, Phys. Rev. E 66, 027106 (2002).
G. Ódor, Phys. Rev. E 67, 016111 (2003).
J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003).
R. Dickman and M.A.F. de Menenzes, Phys. Rev. E 66, 045101 (2002).
K. Park, H. Hinrichsen, and I. Kim, Phys. Rev. E 66, 025101 (2002).
G. Ódor, Phys. Rev. E 67, 056114 (2003).
G. Ódor, Braz. J. Phys. 33, 431 (2003).
M.J. Howard and U.C. Täuber, J. Phys. A 30, 7721 (1997).
G. Ódor, Phys. Rev. E 65, 026121 (2002).
G. Ódor, N. Boccara, and G. Szabó, Phys. Rev. E 48, 3168 (1993).
G. Ódor and A. Szolnoki, Phys. Rev. E 53, 2231 (1996).
N. Menyhárd and G. Ódor, J. Phys. A 28, 4505 (1995).
H.A. Gutowitz, J.D. Victor, and B.W. Knight, Physica D 28, 18 (1987).
R. Dickman, Phys. Rev. A 38, 2588 (1988).
R. Dickman, W.R.M. Rabelo, and G. Ódor, Phys. Rev. E 65, 016118 (2001).
B.P. Lee, J. Phys. A 27, 2633 (1994).
J.L. Cardy and U.C. Täuber, J. Stat. Phys. 90, 1 (1998).
R. Dickman, Phys. Rev. B 40, 7005 (1989); Phys. Rev. A 42, 6985 (1990).
N. Menyhárd and G. Ódor, Phys. Rev. E 68, 056106 (2003).
G. Ódor and N. Menyhárd, Physica D 168, 305 (2002).

[c1] For references see J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).

[c2] H. Berry, Phys. Rev. E 67, 031907 (2003).

[c3] J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).

[c4] H. Hinrichsen, Adv. Phys. 49, 815 (2000).

[c5] G. Ódor, Rev. Mod. Phys (to be published), e-print cond-mat/0205644.

[c6] U. Täuber, Adv. Solid State Phys. 43, 659 (2003).

[c7] P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982).

[c8] E. Carlon, M. Henkel, and U. Schollwöck, Phys. Rev. E 63, 036101 (2001).

[c9] H. Hinrichsen, Phys. Rev. E 63, 036102 (2001).

[c10] G. Ódor, Phys. Rev. E 62, R3027 (2000).

[c11] H. Hinrichsen, Physica A 291, 275 (2001).

[c12] G. Ódor, Phys. Rev. E 63, 067104 (2001).

[c13] J.D. Noh and H. Park, Phys. Rev. E 69, 016122 (2004).

[c14] M. Henkel and U. Schollwöck, J. Phys. A 34, 3333 (2001).

[c15] M. Henkel and H. Hinrichsen, J. Phys. A 34, 1561 (2001).

[c16] K. Park, H. Hinrichsen, and In-mook Kim, Phys. Rev. E 63, 065103(R) (2001).

[c17] G. Ódor, M.A. Santos, and M.C. Marques, Phys. Rev. E 65, 056113 (2002).

[c18] G. Ódor, Phys. Rev. E 65, 026121 (2002).

[c19] K. Park and I. Kim, Phys. Rev. E 66, 027106 (2002).

[c20] G. Ódor, Phys. Rev. E 67, 016111 (2003).

[c21] J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003).

[c22] R. Dickman and M.A.F. de Menenzes, Phys. Rev. E 66, 045101 (2002).

[c23] K. Park, H. Hinrichsen, and I. Kim, Phys. Rev. E 66, 025101 (2002).

[c24] G. Ódor, Phys. Rev. E 67, 056114 (2003).

[c25] G. Ódor, Braz. J. Phys. 33, 431 (2003).

[c26] M.J. Howard and U.C. Täuber, J. Phys. A 30, 7721 (1997).

[c27] G. Ódor, Phys. Rev. E 65, 026121 (2002).

[c28] G. Ódor, N. Boccara, and G. Szabó, Phys. Rev. E 48, 3168 (1993).

[c29] G. Ódor and A. Szolnoki, Phys. Rev. E 53, 2231 (1996).

[c30] N. Menyhárd and G. Ódor, J. Phys. A 28, 4505 (1995).

[c31] H.A. Gutowitz, J.D. Victor, and B.W. Knight, Physica D 28, 18 (1987).

[c32] R. Dickman, Phys. Rev. A 38, 2588 (1988).

[c33] R. Dickman, W.R.M. Rabelo, and G. Ódor, Phys. Rev. E 65, 016118 (2001).

[c34] B.P. Lee, J. Phys. A 27, 2633 (1994).

[c35] J.L. Cardy and U.C. Täuber, J. Stat. Phys. 90, 1 (1998).

[c36] R. Dickman, Phys. Rev. B 40, 7005 (1989); Phys. Rev. A 42, 6985 (1990).

[c37] N. Menyhárd and G. Ódor, Phys. Rev. E 68, 056106 (2003).

[c38] G. Ódor and N. Menyhárd, Physica D 168, 305 (2002).

Physical Review E

Export citation

Export citation

Phase transitions of the binary production $2 \vec{A} 3 A, 4 \vec{A} \emptyset$ model

Abstract

References (38)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Phase transitions of the binary production 2A→3A,4A→∅ model

Abstract

References (38)

Phase transitions of the binary production $2 \vec{A} 3 A, 4 \vec{A} \emptyset$ model