Lattice star and acyclic branched polymer vertex exponents in 3d

Abstract

Numerical values of lattice star entropic exponents ${\gamma }_f$, and star vertex exponents ${\sigma }_f$, are estimated using parallel implementations of the PERM and Wang-Landau algorithms. Our results show that the numerical estimates of the vertex exponents deviate from predictions of the $\epsilon$-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents ${\gamma }_{\mathcal{G}}$ of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the scaling relation $${\gamma }_{\mathcal{G}}-1=\sum _{f\ge 1}{m}_f{\sigma }_f$$ for a comb and two brushes (where $m_f$ is the number of nodes of degree $f$ in the network) using our independent estimates of ${\sigma }_f$.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2008.05622

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Cited by in corpus (1)

• Entropic exponents of grafted lattices stars