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In contrast to the infinite chain, the low-temperature expansion of aone-dimensional free-field Ising model has a strong dependence on boundaryconditions. I derive explicit formula for the leading term of the expansionboth under open and periodic boundary conditions, and show they are related todifferent distributions of partition function zeros on the complex temperatureplane. In particular, when the periodic boundary condition is imposed, theleading coefficient of the expansion grows with size, due to the zerosapproaching the origin.

Low temperature behavior of finite-size one-dimensional Ising model and the partition function zeros