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Nature vs. Nurture in Discrete Spin Dynamics

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Book cover Sojourns in Probability Theory and Statistical Physics - I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 298))

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Abstract

The problem of predictability, or “nature vs. nurture”, in both ordered and disordered Ising systems following a deep quench from infinite to zero temperature is reviewed. Two questions are addressed. The first deals with the nature of the final state: for an infinite system, does every spin flip infinitely often, or does every spin flip only finitely many times, or do some spins flip infinitely often and others finitely often? Once this question is determined, the evolution of the system from its initial state can be studied with attention to the issue of how much information contained in the final state depends on that contained in the initial state, and how much depends on the detailed history of the system. This problem has been addressed both analytically and numerically in several papers, and their main methods, results, and conclusions will be reviewed. The discussion closes with some open problems that remain to be addressed.

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Acknowledgments

I thank my collaborators on various aspects of this work—Reza Gheissari, Jon Machta, Chuck Newman, Paolo Maurilo de Oliveira, Vladas Sidoravicius, Eric Song, Lily Wang, and Jing Ye—for a productive and enjoyable collaboration. And of course, happy birthday (again) to Chuck!

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Authors and Affiliations

  1. Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Daniel L. Stein

  2. NYU-ECNU Institutes of Physics and Mathematical Sciences, NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China

    Daniel L. Stein

  3. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA

    Daniel L. Stein

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Correspondence to Daniel L. Stein .

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Editors and Affiliations

  1. NYU Shanghai, Shanghai, China

    Vladas Sidoravicius

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Stein, D.L. (2019). Nature vs. Nurture in Discrete Spin Dynamics. In: Sidoravicius, V. (eds) Sojourns in Probability Theory and Statistical Physics - I. Springer Proceedings in Mathematics & Statistics, vol 298. Springer, Singapore. https://doi.org/10.1007/978-981-15-0294-1_11

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