A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials

Jose A Cuesta; Angel Sanchez

doi:10.1088/0305-4470/35/10/303

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A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials

Jose A Cuesta·Angel Sanchez

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Abstract

We rigorously prove that a wide class of one-dimensional growth models with onsite periodic potential, such as the discrete sine-Gordon model, have no phase transition at any temperature $T>0$. The proof relies on the spectral analysis of the transfer operator associated to the models. We show that this operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic function of temperature.

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Jose A Cuesta, Angel Sanchez. 2001-12-03. A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials. https://doi.org/10.1088/0305-4470%2F35%2F10%2F303

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