Abstract
We show that it is possible to derive the stationary coverage of an adsorption–desorption process of dimers with diffusional relaxation with a very simple ansatz for the stationary distribution of the process supplemented by a hypothesis of global balance. Our approach is compared to the exact result and we seek to understand its validity within an instance of the model.
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REFERENCES
A. Kolmogoroff, Zur Theorie der Markoffschen Ketten, Math. Ann. 112:155 (1936).
N. G. van Kampen, Stochastic Processes in Physics and Chemistry, Rev. and Enl. Ed. (North-Holland, Amsterdam, 1992).
R. H. Swendsen, Monte Carlo calculation of renormalized coupling parameters, Phys. Rev. Lett. 52:1165 (1984); Monte Carlo calculation of renormalized coupling parameters. I. d=2 Ising models, Phys. Rev. B 30:3866 (1984); Monte Carlo calculation of renormalized coupling parameters. II. d=3 Ising models, Phys. Rev. B 30:3875 (1984); J. H. Berry et al., Exact solutions for perpendicular susceptibilities of kagomé and decorated-kagomé Ising models, Phys. Rev. B 35:8601 (1987); Exact solutions for Ising-model even-number correlations on planar lattices, Phys. Rev. B 37:5193 (1988); D. A. Browne and P. Kleban, Equilibrium statistical mechanics for kinetic phase transitions, Phys. Rev. A 40:1615 (1989); M. J. Oliveira, Coupling constants for stochastic spin systems, Physica A 203:13 (1994).
P. L. Garrido and J. Marro, Effective Hamiltonian description of nonequilibrium spin systems, Phys. Rev. Lett. 62:1929 (1989).
M. D. Grynberg, T. J. Newman, and R. B. Stinchcombe, Exact solutions for stochastic adsorption-desorption models and catalytic surface processes, Phys. Rev. E 50:957 (1994).
M. D. Grynberg and R. B. Stinchcombe, Dynamic correlation functions of adsorption stochastic systems with diffusional relaxation, Phys. Rev. Lett. 74:1242 (1995); Dynamics of adsorption-desorption processes as a soluble problem of many fermions, Phys. Rev. E 52:6013 (1995); Autocorrelation functions of driven reaction-diffusion processes, Phys. Rev. Lett. 76:851 (1996).
G. M. Schütz, Diffusion-annihilation in the presence of a driving field, J. Phys. A: Math. Gen. 28:3405 (1995); Nonequilibrium correlation functions in the A + A → Ø system, Phys. Rev. E 53:1475 (1996).
R. J. Glauber, Time-dependent statistics of the Ising model, J. Math. Phys. 4:294 (1963).
J. G. Amar and F. Family, Diffusion annihilation in one dimension and the kinetics of the Ising model at zero temperature, Phys. Rev. A 41:3258 (1990).
B. U. Felderhof, Spin relaxation of the Ising chain, Rep. Math. Phys. 1:215 (1971); Note on spin relaxation of the Ising chain, Rep. Math. Phys. 2:151 (1971).
R. B. Stinchcombe, M. D. Grynberg, and M. Barma, Diffusive dynamics of deposition-evaporation systems, jamming, and broken symmetries in related quantum-spin models, Phys. Rev. E 47:4018 (1993).
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de Mendonça, J.R.G., de Oliveira, M.J. Stationary Coverage of a Stochastic Adsorption–Desorption Process with Diffusional Relaxation. Journal of Statistical Physics 92, 651–658 (1998). https://doi.org/10.1023/A:1023044822735
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DOI: https://doi.org/10.1023/A:1023044822735