6 research outputs found
Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks
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, controls the transition strength; mean-field theory
applies for but critical exponents are -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 .Comment: 5 pages, 5 figure