Abstract
The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating function method, the general solution for F n , the probability that n consecutive sites be full, is obtained. Some other correlation functions of number operators at nonadjacent sites are also explicitly obtained. It is shown that for a special choice of initial conditions some correlation functions of number operators called full intervals remain uncorrelated.
Similar content being viewed by others
References
G.M. Schütz, Exactly solvable models for many-body systems far from equilibrium, in Phase transitions and critical phenomena, edited by C. Domb, J. Lebowitz (Academic Press, 2000), Vol. 19
M. Henkel, H. Hinrichsen, S. Lübeck, Non-equilibrium phase transitions, in Absorbing phase transitions (Springer, 2008), Vol. 1
M. Henkel, M. Pleimling, Non-equilibrium phase transitions, in Ageing and Dynamical Scaling Far from Equilibrium (Springer, 2010), Vol. 2
F.C. Alcaraz, M. Droz, M. Henkel, V. Rittenberg, Ann. Phys. 230, 250 (1994)
K. Krebs, M.P. Pfannmüller, B. Wehefritz, H. Hinrichsen, J. Stat. Phys. 78, 1429 (1995)
H. Simon, J. Phys. A 28, 6585 (1995)
V. Privman, A.M.R. Cadilhe, M.L. Glasser, J. Stat. Phys. 81, 881 (1995)
M. Henkel, E. Orlandini, G.M. Schütz, J. Phys. A 28, 6335 (1995)
M. Henkel, E. Orlandini, J. Santos, Ann. Phys. 259, 163 (1997)
A.A. Lushnikov, Sov. Phys. JETP 64, 81 (1986) [Zh. Eksp. Teor. Fiz. 91, 1376 (1986)]
M. Alimohammadi, V. Karimipour, M. Khorrami, Phys. Rev. E 57, 6370 (1998)
M. Alimohammadi, V. Karimipour, M. Khorrami, J. Stat. Phys. 97, 373 (1999)
A. Aghamohammadi, M. Khorrami, J. Phys. A 33, 7843 (2000)
M.A. Burschka, C.R. Doering, D. Ben-Avraham, Phys. Rev. Lett. 63, 700 (1989)
D. ben-Avraham, Mod. Phys. Lett. B 9, 895 (1995)
D. ben-Avraham, in Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman (Cambridge University press, 1997), pp. 29–50
D. ben-Avraham, Phys. Rev. Lett. 81, 4756 (1998)
M. Henkel, H. Hinrichsen, J. Phys. A 34, 1561 (2001)
T. Masser, D. ben-Avraham, Phys. Lett. A 275, 382 (2000)
M. Alimohammadi, M. Khorrami, A. Aghamohammadi, Phys. Rev. E 64, 056116 (2001)
M. Khorrami, A. Aghamohammadi, M. Alimohammadi, J. Phys. A 36, 345 (2003)
A. Aghamohammadi, M. Alimohammadi, M. Khorrami, Eur. Phys. J. B 31, 371 (2003)
A. Aghamohammadi, M. Khorrami, Int. J. Mod. Phys. B 18, 204 (2004)
A. Aghamohammadi, M. Khorrami, Eur. Phys. J. B 47, 583 (2005)
M. Mobilia, P.A. Bares, Phys. Rev. E 64, 066123 (2001)
X. Durang, J.-Y. Fortin, D. Del Biondo, M. Henkel, J. Richert, J. Stat. Mech., P04002 (2010)
X. Durang, J.-Y. Fortin, M. Henkel, J. Stat. Mech., P02030 (2011)
G.M. Schütz, J. Stat. Phys. 79, 243 (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Khorrami, M., Aghamohammadi, A. Autonomous models solvable through the full interval method. Eur. Phys. J. B 85, 134 (2012). https://doi.org/10.1140/epjb/e2012-20979-3
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-20979-3