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  • Letter

Exact expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble

Daniel Dantchev1,2,3,4 and Joseph Rudnick2

  • 1Institute of Mechanics, Bulgarian Academy of Sciences, Academic Georgy Bonchev Street, Building 4, BG-1113 Sofia, Bulgaria
  • 2Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
  • 3Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
  • 4IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

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Phys. Rev. E 106, L042103 – Published 27 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.L042103

Abstract

We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble, for three commonly used boundary conditions: periodic, antiperiodic, and Dirichlet. These expressions allow for the determination of fluctuation-induced forces in the canonical ensemble, which we term Helmholtz forces. The thermodynamic expressions and the calculations flowing from them should provide insights into the nature and behavior of fluctuation-induced forces in interesting and as-yet unexplored regimes.

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Phys. Rev. E 106, L042103– Published 27 October, 2022
  • Received 26 July 2022
  • Accepted 7 October 2022
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