论文标题
方格恒星顶点指数的数值估计值
Numerical estimates of square lattice star vertex exponents
论文作者
论文摘要
我们为恒星和方格中的无环均匀分支网络实施了GARM和Wang-Landau算法的并行版本。这些是单分散的分支聚合物的型号，我们估计$ f $ stars的星顶点指数$σ_f$，以及带有梳子和刷子连接的网络的熵指数$γ_\ Mathcal {g} $。我们的结果验证了顶点指数的预测（但未严格证明）的精确值，并测试缩放关系[5] $$γ_ {\ Mathcal {g}}} -1 = \ sum_ {f \ geq 1} m_f \ f \ geq 1} m_f \ f \ f $ f \ f $ f \ f $ for tus Branched网络在两个尺度上。
We implement parallel versions of the GARM and Wang-Landau algorithms for stars and for acyclic uniform branched networks in the square lattice. These are models of monodispersed branched polymers, and we estimate the star vertex exponents $σ_f$ for $f$-stars, and the entropic exponent $γ_\mathcal{G}$ for networks with comb and brush connectivity in two dimensions. Our results verify the predicted (but not rigorously proven) exact values of the vertex exponents and we test the scaling relation [5] $$ γ_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f \, σ_f $$ for the branched networks in two dimensions.
