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29 March 2024
 
  » arxiv » 1507.0223

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Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks
M. Krasnytska ; B. Berche ; Yu. Holovatch ; R. Kenna ;
Date 1 Jul 2015
AbstractThe 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 $lambda=5$.
Source arXiv, 1507.0223
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