Abstract
We present a proof of the exponential convergence to equilibrium of single-spin-flip stochastic dynamics for the two-dimensional Ising ferromagnet in the low-temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions.
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References
R. Holley, Possible rates of convergence in finite range, attractive spin systems,Contemp. Math. 41:215 (1985).
R. Holley, Rapid convergence to equilibrium in one dimensional stochastic Ising models,Ann. Prob. 13:72–89 (1985).
R. Holley and D. Strook,L 2 theory of the stochastic Ising model,Z. Wahr. verw. Geb. 35:87–101 (1976).
M. Aizenman and R. Holley, inPercolation and Ergodic Theory of Infinite Particle Systems, H. Kesten, ed. (Springer-Verlag, 1987).
E. Jordão Neves and R. H. Schonmann, Critical droplets and metastability for a Glauber dynamics at very low temperatures, Preprint, University of Sao Paulo, Brazil.
F. Martinelli, E. Olivieri, and E. Scoppola, On the Swendsen and Wang dynamics II. Critical droplets and homogeneous nucleation at low temperature for the 2-dimensional Ising model, Preprint, Rome (1990).
F. Martinelli, E. Olivieri, and E. Scoppola, On the Swendsen and Wang dynamics I. Exponential convergence to equilibrium, Preprint, Rome (1990).
F. Martinelli, E. Olivieri, and E. Scoppola, Rigorous analysis of low temperature stochastic ising models: Metastability and exponential approach to equilibrium,Europhysics Letter 12, No. 2 (1990).
F. Martinelli, E. Olivieri, and E. Scoppola, On the loss of memory of initial conditions for some stochastic flows, inProceedings of the 2nd Ascona-Como International Conference, “Stochastic Process-Geometry & Physics”, S. Albeverio, ed. (World Scientific, Singapore, 1989).
R. L. Dobrushin and S. B. Shlosman, Constructive criterion for the uniqueness of Gibbs field, inStatistical Physics and Dynamical Systems (Birkhauser, 1985).
T. M. Liggett,Interacting Particle Systems (Springer, Berlin, 1985).
D. A. Huse and D. S. Fisher,Phys. Rev. B 35:6841 (1987).
A. D. Sokal and L. E. Thomas, Absence of mass gap for a class of stochastic contour models,J. Stat. Phys. 51:907 (1988).
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Martinelli, F., Olivieri, E. & Scoppola, E. Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models. J Stat Phys 61, 1105–1119 (1990). https://doi.org/10.1007/BF01014367
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DOI: https://doi.org/10.1007/BF01014367