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Article Dans Une Revue Journal of High Energy Physics Année : 2024

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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hal-04286332 , version 1 (28-06-2024)

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Kay Joerg Wiese, Jesper Lykke Jacobsen. The two upper critical dimensions of the Ising and Potts models. Journal of High Energy Physics, 2024, 05, pp.092. ⟨10.1007/JHEP05(2024)092⟩. ⟨hal-04286332⟩
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