Abstract
In the limit as the volume grows and the temperature vanishes, it is shown that the one-dimensional nearest neighbor ferromagnetic Ising model presents a sharp transition between two different regimes. Fluctuations are studied in one of these regimes and also in the critical case.
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References
J. Adler, D. Stauffer, and A. Aharony, Comparison of bootstrap percolation models,J. Phys. A: Math. Gen. 22:L297-L301 (1989).
M. Aizenman and J. Lebowitz, Metastability effects in bootstrap percolation,J. Phys. A: Math. Gen. 21:3801–3813 (1988).
K. Froböse, Is there a percolation threshold in a cellular automat for diffusion?,J. Stat. Phys. 55:1285–1292 (1989).
B. V. Gnedenko,The Theory of Probability (Mir, Moscow, 1978) [English translation].
E. J. Neves and R. H. Schonmann, Critical droplets and metastability for a Glauber dynamics at very low temperature, preprint (1989).
H. L. Royden,Real Analysis, 2nd ed. (Macmillan, New York, 1968).
R. H. Schonmann, On the behavior of some cellular automata related to bootstrap percolation, preprint (1989).
R. H. Schonmann, Critical points of two dimensional bootstrap percolation like cellular automata,J. Stat. Phys. (to appear).
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Schonmann, R.H., Tanaka, N.I. One-dimensional caricature of phase transition. J Stat Phys 61, 241–252 (1990). https://doi.org/10.1007/BF01013963
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DOI: https://doi.org/10.1007/BF01013963