TY - JOUR

T1 - Rods to self-avoiding walks to trees in two dimensions

AU - Camacho, Carlos J.

AU - Fisher, Michael E.

AU - Straley, Joseph P.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.46.6300

DO - 10.1103/PhysRevA.46.6300

M3 - Article

AN - SCOPUS:0005057958

SN - 1050-2947

VL - 46

SP - 6300

EP - 6310

JO - Physical Review A

JF - Physical Review A

IS - 10

ER -