Abstract
We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n α interactions, where 1<α≦2. In particular for the often studied case of α=2 we have an upper bound onT c which is less than theT c found by a number of approximation techniques. Also for the case where α is small, such as α=1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.
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Monroe, J.L. Upper bounds onT c for one-dimensional Ising systems. J Stat Phys 76, 1505–1510 (1994). https://doi.org/10.1007/BF02187074
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DOI: https://doi.org/10.1007/BF02187074