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arXiv · 2410.01234

Phase Transition in Long-Range $q-$state Models via Contours. Clock and Potts Models with Fields

Lucas Affonso·Rodrigo Bissacot·Gilberto Faria·Kelvyn Welsch
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Abstract

Using the group structure of the state space of $q-$state models, a new definition of contour for long-range spin-systems in $\Z^d$ ($d\geq 2$), and a multidimensional version of Fr\"{o}hlich-Spencer contours, we prove phase transition for a class of ferromagnetic long-range systems which includes the Clock and Potts models. Our arguments work for the entire region of exponents of regular power-law interactions, namely $\alpha > d$, and for any $q \geq 2$. As an application, we prove phase transition for Potts models with decaying fields when the field decays fast enough and in the presence of a random external field.

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Lucas Affonso, Rodrigo Bissacot, Gilberto Faria, Kelvyn Welsch. 2024-10-02. Phase Transition in Long-Range $q-$state Models via Contours. Clock and Potts Models with Fields. https://arxiv.org/abs/2410.01234

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