Rods to self-avoiding walks to trees in two dimensions

Carlos J. Camacho, Michael E. Fisher, Joseph P. Straley

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The mean-square radius of gyration RG2 and a shape parameter =RGmin2/RGmax2 are studied as a function of the number of bonds, bends, and branches of self-avoiding lattice trees on the square, triangular, and honeycomb lattices. We identify the universality classes, and exhibit the crossover scaling functions that connect them. We find (despite doubts recently raised) that there is a universal crossover from rods to self-avoiding walks, embodied in RG2∼N2U(Nw), where w(z) is an appropriately chosen nonlinear scaling field reducing to the stiffness fugacity z as z→0; that ''rigid trees'' (which are bond clusters that branch but do not bend) are in the same universality class as branched polymers or free trees; that the crossover from rods to rigid trees has the universal form RG2∼N2W(Ny2), where y is the branching fugacity; and that the crossover from self-avoiding walks to branched polymers has the universal form RG2∼Ns2νY(Nyφ), with νs=3/4 and φ=55/32.

Original languageEnglish
Pages (from-to)6300-6310
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number10
StatePublished - 1992

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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