# Groupe de Physique Statistique

## Equipe 106, Institut Jean Lamour

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### Articles dans des revues à comité de lecture

 Fisher’s scaling relation above the upper critical dimension Kenna R., Berche B. EPL 105 (2014) 26005 DOI : 10.1209/0295-5075/105/26005 ArXiv : arxiv:1412.6926 [PDF] Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension $d_c$. However, it has long been known that numerical simulations deliver a negative value for the anomalous dimension there. Here, the apparent discrepancy is attributed to a distinction between the system-length and correlation- or characteristic-length scales. On the latter scale, the anomalous dimension indeed vanishes above $d_c$ and Fisher's relation holds in its standard form. However, on the scale of the system length, the anomalous dimension is negative and Fisher's relation requires modification. Similar investigations at the upper critical dimension, where dangerous irrelevant variables become marginal, lead to an analogous pair of Fisher relations for logarithmic-correction exponents.