The two upper critical dimensions of the Ising and Potts models
Résumé
We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field $\Phi^\alpha$. For the Ising model ($Q=2$), the field theory for the spins has upper critical dimension $d_{\rm c}^{\rm spin}=4$, whereas for the clusters it has $d_{\rm c}^{\rm cluster}=6$. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory theory for $d$ within $4
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Soumis le : mercredi 15 novembre 2023-09:46:51
Dernière modification le : vendredi 7 juin 2024-15:37:34
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- HAL Id : hal-04286332 , version 1
- ARXIV : 2311.01529
- DOI : 10.1007/JHEP05(2024)092
- INSPIRE : 2718872
Citer
Kay Joerg Wiese, Jesper Lykke Jacobsen. The two upper critical dimensions of the Ising and Potts models. JHEP, 2024, 05, pp.092. ⟨10.1007/JHEP05(2024)092⟩. ⟨hal-04286332⟩
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