Classical XY Model in 1.99 Dimensions

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.

LaTeX 8 pages, no figures

References in corpus (1)

• Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

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