Abstract
This is not primarily a paper about applications of mathematics to statistical physics, but rather a report on how a particular problem of statistical physics has resulted in an extensive mathematical theory. The problem alluded to is the computation of the spontaneous magnetizationM o (T) of the two-dimensional Ising model with nearest-neighbor interactions, whose solution for temperaturesT below the Curie pointT c was given by the famous formula of Lars Onsager in 1948. The theory grown out of this formula is the edifice of Toeplitz determinants, matrices, and operators.
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Böttcher, A. The Onsager formula, the fisher-hartwig conjecture, and their influence on research into Toeplitz operators. J Stat Phys 78, 575–584 (1995). https://doi.org/10.1007/BF02183366
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DOI: https://doi.org/10.1007/BF02183366