标题： 复网络上伊辛相变的李-杨圆定理的破坏 显示英文标题

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

摘要： 在度分布按$p(K)\sim K^{-\lambda}$代数方式衰减的退火复杂网络上的伊辛模型，在$\lambda> 3$时具有有限温度下的二阶相变。在没有空间维度的情况下，$\lambda$控制转变强度；当$\lambda >5$时，均场理论适用，但如果$\lambda < 5$，临界指数则依赖于$\lambda$。这里我们表明，与规则晶格类似，著名的李-杨圆定理适用于前一种情况。然而，与规则晶格上该定理独立于维度不同，当$\lambda < 5$时，圆定理在复杂网络上失效。我们讨论了这一结果在相变和临界现象的理论和实验中的重要性。 我们还研究了两种情况下的有限尺寸标度的Lee-Yang零点，以及在$\lambda=5$处出现的乘法对数修正。 显示英文摘要

摘要： 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 $\lambda=5$.