Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914343028785152 |
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| author | Campa, Alessandro Hovhannisyan, Vahan Ruffo, Stefano Trombettoni, Andrea |
| author_facet | Campa, Alessandro Hovhannisyan, Vahan Ruffo, Stefano Trombettoni, Andrea |
| contents | We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-$1$ Blume-Emery-Griffiths model and solving it by using an Hubbard-Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling $K$ and the temperature $T$. We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase-transition lines. We also prove that, when the nearest-neighbour coupling $K$ is large and negative, the first-order transition temperature becomes asymptotically independent of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction Campa, Alessandro Hovhannisyan, Vahan Ruffo, Stefano Trombettoni, Andrea Statistical Mechanics We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-$1$ Blume-Emery-Griffiths model and solving it by using an Hubbard-Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling $K$ and the temperature $T$. We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase-transition lines. We also prove that, when the nearest-neighbour coupling $K$ is large and negative, the first-order transition temperature becomes asymptotically independent of $K$. |
| title | Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.02930 |