# Groupe de Physique Statistique

## Equipe 106, Institut Jean Lamour

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### Articles dans des revues à comité de lecture

 Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks M. Krasnytska, B. Berche, Yu. Holovatch, R. Kenna EPL 111 (2015) 60009 DOI : 10.1209/0295-5075/111/60009 ArXiv : arxiv:1507.00223 [PDF] The Ising model on annealed complex networks with degree distribution decaying algebraically as $p(K)\sim K^{-\lambda}$ has a second-order phase transition at finite temperature if $\lambda >3$. In the absence of space dimensionality, $\lambda$ controls the transition strength; mean-field theory applies for $\lambda >5$ but critical exponents are $\lambda-$dependent if $\lambda<5$. Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when $\lambda<5$. We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at $\lambda=5$.