Abstract
Validity of two scaling relations β = ν ∥ θ and z = ν ∥ / ν ⊥ widely known in absorbing phase transitions is studied for the conserved lattice gas (CLG) model and the conserved threshold transfer process CTTP) both in one dimension. For the CLG model, it is found that both relations hold when the critical exponents calculated from the all-sample average density of active particles are considered. For the CTTP model, various exponents are calculated via Monte Carlo simulations and they are confirmed by the off-critical scaling and the finite-size scaling analyses. The exponents estimated from the all-sample averages again satisfy both relations. These observations are in strict disagreement with earlier observations in two dimensions [Phys. Rev. Lett. 85, 1803 (2000); Phys Rev. E 68, 056102 (2003)] but support the more recent observation for the CLG model [Phys. Rev. E 78, 040103(R) (2008)].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Marro, J., Dickman, R.: Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge (1999)
Hinrichsen, H.: Adv. Phys. 49, 815 (2000); Hinrichsen, H.: Braz. J. Phys. 30, 69 (2000)
Ben-Avraham, D., Havlin, S.: Diffusion and Reaction in Fractals and Disordered Systems. Cambridge University Press, Cambridge (2000)
Ódor, G.: Rev. Mod. Phys. 76, 663 (2004)
Janssen, H.K.: Z. Phys. B: Condens. Matt. 42, 151 (1981)
Grassberger, P.: Z. Phys. B Condens. Matt. 47, 365 (1982)
Jensen, I., Dickman, R.: Phys. Rev. E 48, 1710 (1993); Jensen, I.: J. Phys. A 27, L61 (1994)
Muñoz, M.A., Grinstein, G., Dickamn, R., Livi, R.: Phys. Rev. Lett. 76, 451 (1996)
Takayasu, H., Tretyakov, A.Y.: Phys. Rev. Lett. 68, 3060 (1992)
Jensen, I.: Phys. Rev. E 50, 3623 (1994)
Kwon, S., Park, H.: Phys. Rev. E 52, 5955 (1995)
Cardy, J., Tauber, U.C.: Phys. Rev. Lett. 77, 4780 (1996)
For the bosonic mversion of the PCPD model, Howard, M.J., Täuber, J.C.: J. Phys. A 30, 7721 (1997); for the fermionic version, Carton, E., Henkel, M., Schollwöck, U.: Phys. Rev. E 63, 36101 (2001)
Kochelkoren, J., Chate, H.: Phys. Rev. Lett. 90, 125701 (2002)
Noh, J.D., Park, H.: Phys. Rev. E 69, 016122 (2004)
Hinrichsen, H.: Physica A 361, 457 (2006)
Park, K., Hinrichsen, H., Kim, I.-M.: Phys. Rev. E 66, 025101 (2002)
Ódor, G.: Phys. Rev. E 67, 056114 (2003)
Rossi, M., Pastor-Satorras, R., Vespignani, A.: Phys. Rev. Lett. 85, 1803 (2000)
Manna, S.S.: J. Phys. A 24, L363 (1991)
Dhar, D.: Physica 263A, 4 (1999)
Vespignani, A., Dickman, R., Muñoz, M.A., Zapperi, S.: Phys. Rev. E 62, 4564 (2000)
Stanley, H.E.: Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, London (1971)
Amit, D.J.: Field Theory, the Renormalization Group, and Critical Phenomena. World Scientific, Singapore (1984)
Vespignani, A., Dickman, R., Muñoz, M.A., Zapperi, S.: Phys. Rev. Lett. 81, 5676 (1998); Dickman, R., Vespignani, A., Zapperi, S.: Phys. Rev. E 57, 5095 (1998)
Lübeck, S., Misra, A.: Eur. Phys. J. B 26, 75 (2002)
Lübeck, S., Heger, P.C.: Phys. Rev. E 68, 56102 (2003); Lübeck, S.: ibid 66, 046114 (2002)
Lee, S.-G., Lee, S.B.: Phys. Rev. E 77, 021113 (2008)
Lee, S.B., Lee, S.-G.: Phys. Rev. E 78, 040103(R) (2008)
de Oliveira, M.J.: Phys. Rev. E 71, 016112 (2005)
Lübeck, S.: Phys. Rev. E 64, 16123 (2001); Lübeck, S.: ibid 66, 46114 (2002)
Dickman, R., Alava, M., Muñoz, M.A., Peltola, J., Vespignani, A., Zapperi, S.: Phys. Rev. E 64, 056104 (2001)
Lee, S.-G., Lee, S.B.: Phys. Rev. E 77, 041122 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Lee, SG., Lee, S.B. (2009). Scaling Relations in Absorbing Phase Transitions with a Conserved Field in One Dimension. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_83
Download citation
DOI: https://doi.org/10.1007/978-3-642-02466-5_83
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02465-8
Online ISBN: 978-3-642-02466-5
eBook Packages: Computer ScienceComputer Science (R0)