论文标题
复杂的网络增长模型：非Xtentimentive统计力学与随机几何形状之间的同构
Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry
论文作者
论文摘要
In the realm of Boltzmann-Gibbs statistical mechanics there are three well known isomorphic connections with random geometry, namely (i) the Kasteleyn-Fortuin theorem which connects the $λ\to 1$ limit of the $λ$-state Potts ferromagnet with bond percolation, (ii) the isomorphism which connects the $λ\to 0$ limit of the $λ$ - 状态Potts Ferromagnet具有随机电阻网络，以及（iii）De Gennes同构，将$ n \与$ n $ vector Ferromagnet的$ n \ 0 $限制连接起来，并在线性性聚合物中进行自我避免随机行走。我们在这里提供了有力的数值证据，表明类似的同构似乎会出现，将能量$ q $ - 表达分布$ \ propto e_q^{ - β_q\ varepsilon} $（$ q = 4/3 $ = 4/3 $和$β_Q_Q__Q______0= 10/3 $在简单的preight prectropy上，$ snopropy opropy opropy opopy opropy opoproy opropy opopy opoproy，通过指数分配的加权链接附件，$ω_0$是特征重量。
In the realm of Boltzmann-Gibbs statistical mechanics there are three well known isomorphic connections with random geometry, namely (i) the Kasteleyn-Fortuin theorem which connects the $λ\to 1$ limit of the $λ$-state Potts ferromagnet with bond percolation, (ii) the isomorphism which connects the $λ\to 0$ limit of the $λ$-state Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism which connects the $n \to 0$ limit of the $n$-vector ferromagnet with self-avoiding random walk in linear polymers. We provide here strong numerical evidence that a similar isomorphism appears to emerge connecting the energy $q$-exponential distribution $\propto e_q^{-β_q \varepsilon}$ (with $q=4/3$ and $β_q ω_0 =10/3$) optimizing, under simple constraints, the nonadditive entropy $S_q$ with a specific geographic growth random model based on preferential attachment through exponentially-distributed weighted links, $ω_0$ being the characteristic weight.
