Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

¹ Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine - 79011 Lviv, Ukraine
² Institut Jean Lamour, CNRS/UMR 7198, Groupe de Physique Statistique, Université de Lorraine BP 70239, F-54506 Vandœuvre-les-Nancy Cedex, France
³ Applied Mathematics Research Centre, Coventry University - Coventry, CV1 5FB, UK

Received: 1 July 2015
Accepted: 22 September 2015

Abstract

The Ising model on annealed complex networks with degree distribution decaying algebraically as has a second-order phase transition at finite temperature if . In the absence of space dimensionality, λ controls the transition strength; classical mean-field exponents apply for but critical exponents are λ-dependent if . 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 . 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 .