arXiv subjects

S Campbell

Publications and source records attributed to S Campbell.

3 recordsLinked to original sources

arXiv2021

Lattice star and acyclic branched polymer vertex exponents in 3d

Numerical values of lattice star entropic exponents $γ_f$, and star vertex exponents $σ_f$, 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 $ε$-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents $γ_\mathcal{G}$ of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the scaling relation $$ γ_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f \, σ_f $$ 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 $σ_f$.

cond-mat.stat-mech↗

arXiv2021

Numerical estimates of square lattice star vertex exponents

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.

cond-mat.stat-mech↗

arXiv2020

Parallel PERM

We develop and implement a parallel flatPERM algorithm \cite{G97,PK04} with mutually interacting parallel flatPERM sequences and use it to sample self-avoiding walks in 2 and 3 dimensions. Our data show that the parallel implementation accelerates the convergence of the flatPERM algorithm. Moreover, increasing the number of interacting flatPERM sequences (rather than running longer simulations) improves the rate of convergence. This suggests that a more efficient implementation of flatPERM will be a massively parallel implementation, rather than long simulations of one, or a few parallel sequences. We also use the algorithm to estimate the growth constant of the self-avoiding walk in two and in three dimensions using simulations over 12 parallel sequences. Our best results are \[ μ_d = \cases{ 2.6381585(1), & \hbox{if $d=2$}; \cr 4.684039(1), & \hbox{if $d=3$}. } \]

cond-mat.stat-mech↗