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

TL;DR

This paper investigates the Lee-Yang circle theorem's validity for Ising models on complex networks, revealing its violation for certain degree distributions and analyzing finite-size effects and critical phenomena.

Contribution

It demonstrates the violation of the Lee-Yang circle theorem on complex networks with degree exponent less than 5, contrasting with regular lattice behavior.

Findings

Lee-Yang circle theorem holds for >5

The theorem fails for <5 on complex networks

Finite-size scaling and logarithmic corrections are analyzed at =5

Abstract

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 $\lambda=5$.