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Exact expressions for the partition function of the one-dimensional Ising model in the fixed-M ensemble
Daniel Dantchev1,2,3,4, Joseph Rudnick2
1Institute of Mechanics, Bulgarian Academy of Sciences, Academic Georgy Bonchev Street, Building 4, BG-1113 Sofia, Bulgaria.
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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