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Relaxation Times for Stochastic Ising Models in the Limit of Vanishing External Field at Fixed Low Temperatures

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Cellular Automata and Cooperative Systems

Part of the book series: NATO ASI Series ((ASIC,volume 396))

Abstract

Results are stated concerning the asymptotic growth of relaxation times for basic stochastic Ising models as the external field vanishes.

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References

  • Aizenman, M. and Lebowitz, J.: 1988, ‘Metastability effects in bootstrap percolation’, Journal of Physics A: Mathematics and General, 21, 3801.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Binder, K. and Miiller-Krumbhaar, H.: 1974, ‘Investigation of metastable states and nucleation in the kinetic Ising model’, Physical Review B, 9, 2328.

    Article  ADS  Google Scholar 

  • Capocaccia, D., Cassandro, M. and Olivieri, E.: 1974, ‘A study of metastability in the Ising model’, Communications in Mathematical Physics, 39, 185.

    Article  MathSciNet  ADS  Google Scholar 

  • Cassandro, M., Galves, A., Olivieri, E. and Vares, M.E.: 1984, ‘Metastable behavior of stochastic dynamics: a pathwise approach’, Journal of Statistical Physics, 35, 603.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Jerrum, M. and Sinclair, A.: 1989, ‘Approximating the permanent’, SIAM Journal of Computing, 18, 1149.

    Article  MathSciNet  MATH  Google Scholar 

  • Liggett, T.M.: 1985, Interacting Particle Systems, Springer, New York.

    Book  MATH  Google Scholar 

  • Martirosyan, D. G.: 1987, ‘Theorems on strips in the classical Ising ferromagnetic model’, Soviet Journal of Contemporary Mathematical Analysis, 22, 59.

    Google Scholar 

  • Neves, E.J. and Schonmann, R.H.: 1991, ‘Critical droplets and metastability for a Glauber dynamics at very low temperatures’, Communications in Mathematical Physics, 137, 209.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Neves, E.J. and Schonmann, R.H.: 1992, ‘Behavior of droplets for a class of Glauber dynamics at very low temperature’, Probability Theory and Related Fields ,91, 331.

    Article  MathSciNet  MATH  Google Scholar 

  • Penrose, O. and Lebowitz, J.: 1987, ‘Towards a rigorous molecular theory of metastability’, In Fluctuation Phenomena, second edition, E. Montroll, and J. Lebowitz, J. (eds.) North-Holland Physics Publishing, Amsterdam.

    Google Scholar 

  • Sinclair, A. and Jerrum, M.: 1989, ‘Approximate counting, uniform generation and rapidly mixing Markov chains’, Information and Computation, 82, 93.

    Article  MathSciNet  MATH  Google Scholar 

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© 1993 Springer Science+Business Media Dordrecht

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Schonmann, R.H. (1993). Relaxation Times for Stochastic Ising Models in the Limit of Vanishing External Field at Fixed Low Temperatures. In: Boccara, N., Goles, E., Martinez, S., Picco, P. (eds) Cellular Automata and Cooperative Systems. NATO ASI Series, vol 396. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1691-6_45

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  • DOI: https://doi.org/10.1007/978-94-011-1691-6_45

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4740-1

  • Online ISBN: 978-94-011-1691-6

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