https://doi.org/10.1140/epjb/s10051-026-01124-3
Research - Statistical and Nonlinear Physics
Phase transitions and ensemble inequivalence in the generalized Curie–Weiss model with quartic interaction
School of Physics, Southeast University, 211189, Nanjing, Jiangsu Province, China
a
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Received:
18
November
2025
Accepted:
9
January
2026
Published online:
29
January
2026
We investigate the thermodynamic properties of a generalized Curie–Weiss model incorporating both conventional pairwise spin interactions and an additional quartic four-body interaction term with coupling strength I. Through exact analysis in both canonical and microcanonical ensembles, we demonstrate that this minimalistic model exhibits rich phase behavior including continuous and discontinuous phase transitions, ensemble inequivalence, and a tricritical point at 
. In the canonical ensemble, the transition changes from second order to first order as the quartic coupling I increases beyond the tricritical value. The microcanonical ensemble reveals additional anomalous features including negative specific heat and temperature jumps at first-order transitions. The model provides a paradigmatic example of how simple mean-field systems with higher order interactions can capture the complex phenomenology of long-range interacting systems, including ergodicity breaking and ensemble inequivalence, without requiring spatial complexity.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
