Are there really phase transitions in 1-d heat conduction models?

Lei Yang; Peter Grassberger

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arXiv · cond-mat/0306173

Are there really phase transitions in 1-d heat conduction models?

Lei Yang·Peter Grassberger

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Abstract

Recently, it has been claimed (O. V. Gendelman and A. V. Savin, Phys. Rev. Lett. {\bf 84}, 2381 (2000); A.V.Savin and O.V.Gendelman, arXiv: cond-mat/0204631 (2002)) that two nonlinear classical 1-d lattice models show transitions, at finite temperatures, where the heat conduction changes from being finite to being infinite. These are the well known Frenkel-Kontorova (FK) model and a model for coupled rotators. For the FK model we give strong theoretical arguments why such a phase transition is not to be expected. For both models we show numerically that the effects observed by Gendelman {\it et al.} are not true phase transitions but are rather the expected cross-overs associated to the conductivity divergence as $T\to 0$ and (for the FK model) $T\to\infty$.

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Lei Yang, Peter Grassberger. 2003-06-06. Are there really phase transitions in 1-d heat conduction models?. https://arxiv.org/abs/cond-mat/0306173

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