Lubensky, Tom C
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Publication Electrostatic Repulsion of Positively Charged Vesicles and Negatively Charged Objects(1999-03-01) Aranda-Espinoza, Helim; Chen, Yi; Lubesnky, T C; Dan, Nily; Nelson, Philip C; Ramos, Lauren; Weitz, D. AA positively charged, mixed bilayer vesicle in the presence of negatively charged surfaces (for example, colloidal particles) can spontaneously partition into an adhesion zone of definite area, and another zone that repels additional negative objects. Although the membrane itself has nonnegative charge in the repulsive zone, negative counterions on the interior of the vesicle spontaneously aggregate there, and present a net negative charge to the exterior. Beyond the fundamental result that oppositely charged objects can repel, our mechanism helps explain recent experiments on surfactant vesicles.Publication Direct Determination of DNA Twist-Stretch Coupling(1996-11-01) Kamien, Randall; Lubensky, Tom; Nelson, Philip C; O'Hern, Corey S.The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this important material parameter. We extract its value from a recent experiment of Strick et al. [Science 271 (1996) 1835] and find rough agreement with an independent experimental estimate recently given by Marko. We also present a very simple microscopic theory predicting a value comparable to the one observed.Publication Critical Properties of Spin-Glasses(1976-02-23) Harris, A. Brooks; Lubensky, Thomas C; Chen, Jing-HueiThe critical properties of the model of a spin-glass proposed by Edwards and Anderson are studied using the renormalization group. The critical exponents are calculated in 6−ε spatial dimensions. It is argued that a tricritical point can exist where the nonordering field is the skewness of the distribution of J.Publication ε Expansion for the Conductivity of a Random Resistor Network(1984-08-20) Harris, A. Brooks; Lubensky, Tom C.; Kim, SoobangWe present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)νp+ζ, where νp is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously paradoxical results concerning resistor networks and shows that the Alexander-Orbach relation breaks down at order ε.Publication Flux Phases in Two-Dimensional Tight-Binding Models(1989-08-01) Harris, A. Brooks; Lubensky, Tom C; Mele, Eugene JUsing a gauge-invariant tight-binding model on a rigid square lattice, we discuss the transition between a low-temperature flux phase in which orbital magnetic moments alternate antiferromagnetically in sign from plaquette to plaquette and a normal metallic phase. The order parameter, which may be chosen to be the magnetic flux penetrating a plaquette, goes continuously to zero at the transition. We also consider similar phases in a model with m spin colors antiferromagnetically exchange coupled.Publication Connection Between Percolation and Lattice Animals(1981-04-15) Harris, A. Brooks; Lubensky, Thomas CAn n-state Potts lattice gas Hamiltonian is constructed whose partition function is shown to reproduce in the limit n→0 the generating function for the statistics of either lattice animals or percolating clusters for appropriate choices of potentials. This model treats an ensemble of single clusters terminated by weighted perimeter bonds rather than clusters distributed uniformly throughout the lattice. The model is studied within mean-field theory as well as via the ε expansion. In general, cluster statistics are described by the lattice animal's fixed point. The percolation fixed point appears as a multicritical point in a space of potentials not obviously related to that of the usual one-state Potts model.Publication Randomly Diluted xy and Resistor Networks Near the Percolation Threshold(1987-05-01) Harris, A. Brooks; Lubensky, Thomas CA formulation based on that of Stephen for randomly diluted systems near the percolation threshold is analyzed in detail. By careful consideration of various limiting procedures, a treatment of xy spin models and resistor networks is given which shows that previous calculations (which indicate that these systems having continuous symmetry have the same crossover exponents as the Ising model) are in error. By studying the limit wherein the energy gap goes to zero, we exhibit the mathematical mechanism which leads to qualitatively different results for xy-like as contrasted to Ising-like systems. A distinctive feature of the results is that there is an infinite sequence of crossover exponents needed to completely describe the probability distribution for R(x,x’), the resistance between sites x and x’. Because of the difference in symmetry between the xy model and the resistor network, the former has an infinite sequence of crossover exponents in addition to those of the resistor network. The first crossover exponent φ1=1+ε/42 governs the scaling behavior of R(x,x’) with ‖x-x’‖≡r: [R(x,x’)]c~xφ1/ν, where [ ]c indicates a conditional average, subject to x and x’ being in the same cluster, ν is the correlation length exponent for percolation, and ε=6-d, where d is the spatial dimensionality. We give a detailed analysis of the scaling properties of the bulk conductivity and the anomalous diffusion constant introduced by Gefen et al. Our results show conclusively that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, at least in high spatial dimension. We also evaluate various amplitude ratios associated with susceptibilities, χn involving the nth power of the resistance R(x,x’), e.g., limp→pcχ2χ0/χ12=2[1(19ε/420)]. In an appendix we outline how the calculation can be extended to treat the diluted m-component spin model for m>2. As expected, the results for φ1 remain valid for m>2. The techniques described here have led to several recent calculations of various infinite families of exponents.Publication Renormalization-Group Treatment of the Random Resistor Network in 6−ε Dimensions(1978-02-01) Harris, A. Brooks; Dasgupta, Chandan; Lubensky, Thomas CWe consider a hypercubic lattice in which neighboring points are connected by resistances which assume independently the random values σ>−1 and σ<−1 with respective probabilities p and 1−p. For σ<=0 the lattice is viewed as consisting of irreducible nodes connected by chains of path length L. This geometrical length is distinct from the characteristic length Lr which sets a scale of resistance in the random network or Lm which sets a scale of effective exchange in a dilute magnet. Near the percolation concentration pc one sets L~|p−pc|−ζ, Lr~|p−pc|−ζr and Lm~|p−pc|−ζm. Stephen and Grest (SG) have already shown that ζm=1+o(ε2) for spatial dimensionality d=6−ε. Here we show in a way similar to SG that ζr=1+o(ε2). Thus it is possible that ζm=ζr=1 for a continuous range of d below 6. However, increasing evidence suggests that this equality does not hold for d<4, and in particular a calculation in 1+ε dimensions analogous to that of SG for ζm does not seem possible.Publication Renormalization-Group Approach to the Critical Behavior of Random-Spin Models(1974-12-23) Harris, A. Brooks; Lubensky, Tom C.A renormalization-group technique is used to study the critical behavior of spin models in which each interaction has a small independent random width about its average value. The cluster approximation of Niemeyer and Van Leeuwen indicates that the two-dimensional Ising model has the same critical behavior as the homogeneous system. The ε expansion for n-component continuous spins shows that this behavior holds to first order in ε for n>4. For n<4, there is a new stable fixed point with 2ν=1+[3n/16(n−1)]ε.Publication Renormalization-Group Approach to Percolation Problems(1975-08-11) Harris, A. Brooks; Lubensky, Thomas C; Holcomb, William K; Dasgupta, ChandanThe relation between the s-state Ashkin-Teller-Potts (ATP) model and the percolation problem given by Fortuin and Kasteleyn is used to formulate a renormalization-group treatment of the percolation problem. Both an ε expansion near 6 spatial dimensions and cluster approximations for the recursion relations of a triangular lattice are used. Series results for the ATP model are adapted to the percolation problem.