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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 | 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 $lambda=5$. | Source: | arXiv, 1507.0223 | Services: | Forum | Review | PDF | Favorites |
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