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arXiv · 2207.01134

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

Daniel Dantchev·Joseph Rudnick
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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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Daniel Dantchev, Joseph Rudnick. 2022-07-03. Exact expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble. https://doi.org/10.1103/physreve.106.l042103

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