Abstract
We consider the Potts model in \(\mathbb R^d\), \(d\ge 2\), with \(q \ge 3\) states and prove that for all values of the inverse temperature \(\beta \) which are small enough there is a critical value \(z_c(\beta )\) of the fugacity so that at \((\beta ,z_c(\beta ))\) there are \(q+1\) extremal DLR measures (thus the phase transition is of first order). The first q have a spin which appears with higher frequency than the other spins while in the last one all the spins have the same frequency, moreover the particle density is strictly smaller than in the first q states.
This is a preview of subscription content, log in via an institution to check access.
References
De Masi, A., Merola, I., Presutti, E., Vignaud, Y.: Potts models in the continuum. Uniqueness and exponential decay in the restricted ensembles. J. Stat. Phys. 133, 281–345 (2008)
De Masi, A., Merola, I., Presutti, E., Vignaud, Y.: Coexistence of ordered and disordered phases in Potts models in the continuum. J. Stat. Phys. 134, 243 (2009)
Georgii, H.O.: Salvador miracle-sole, Jean Ruiz, Valentin Zagrebnov. Mean field theory of the potts gas. J. Phys. A 39, 9045–9053 (2006)
Georgii, H.O., Häggstrom, O.: Phase transitions in continuum Potts models. Commun. Math. Phys. 81, 507–528 (1996)
Ruelle, D.: Existence of a phase transition in a continuous classical system. Phys. Rev. Lett. 27, 1040–1041 (1971)
Sinai, Y.G.: Theory of Phase Transitions Rigorous Results. Pergamon Press, Oxford (1982)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Ruelle and Sinai.
Rights and permissions
About this article
Cite this article
Cassandro, M., Presutti, E. A Note on First Order Phase Transitions in the Continuum. J Stat Phys 162, 994–996 (2016). https://doi.org/10.1007/s10955-015-1435-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-015-1435-2