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Journal of Statistical Physics

, Volume 171, Issue 3, pp 449–461 | Cite as

Subexponentially Growing Hilbert Space and Nonconcentrating Distributions in a Constrained Spin Model

  • Jason R. Webster
  • Michael Kastner
Article

Abstract

Motivated by recent experiments with two-component Bose–Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an “order parameter” may be present.

Keywords

Fully-connected spin model Canonical ensemble Concentration of measure 

Notes

Acknowledgements

The authors acknowledge useful discussions with Markus Oberthaler and Hugo Touchette. J.R.W. acknowledges financial support through the internship programme of the National Institute for Theoretical Physics (South Africa). M.K. acknowledges financial support from the National Research Foundation of South Africa via the Competitive Programme for Rated Researchers.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics, Institute of Theoretical PhysicsUniversity of StellenboschStellenboschSouth Africa
  2. 2.National Institute for Theoretical Physics (NITheP)StellenboschSouth Africa

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