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Classical XY Model in 1.99 Dimensions

Tohru Koma·Hal Tasaki
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Abstract

We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low temperature phase is characterized by stretched exponential decay of correlations. We prove an exponentially decaying upper bound for the two-point correlation functions at non-zero temperatures, thus excluding the possibility of such a phase transition.

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Tohru Koma, Hal Tasaki. 1997-08-18. Classical XY Model in 1.99 Dimensions. https://doi.org/10.1103/physrevlett.74.3916

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