Harris, A. Brooks
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Publication Central-Force Models Which Exhibit a Splay-Rigid Phase(1989-10-01) Wang, Jian; Harris, A. BrooksTwo models, one random the other periodic, are described which exhibit splay rigidity but are not rigid with respect to compression. The random model is based on a periodic lattice of rhombuses whose sides consist of central-force springs, which is perturbed in the following way: rhombuses can have diagonal central force struts with probability y or they can have one of the horizontal springs removed with probability x. For x,y≪1 we are led to consider a long-ranged anisotropic percolation process which is solved exactly on a Cayley tree. We show that for y/x near 2 the compressional rigidity of this system is zero but the Frank elastic constant, K, describing splay rigidity is nonzero. This is the first example of a percolation model for which this phenomenon, suggested earlier, is conclusively established. For y/x≳2 √2 the system has nonzero bulk and shear moduli. We also study the excitation spectrum for a periodic model which possesses only splay rigidity and obtain a libron dispersion relation ω=cSq, where q is the wave vector and cS∼(K/ρ)1/2, where ρ is the mass density. These results are generalized to obtain a scaling form for cS and the density of states of the random model which is valid when the correlation length for compressional rigidity becomes large.Publication Electric-Field Control of a Magnetic Phase Transition in Ni3V2O8(2009-04-22) Kharel, Parashu R; Sudakar, Chandran; Dixit, Ambesh V; Harris, A. Brooks; Naik, Ratna; Lawes, Gavin JWe report on the electric-field tuning of a magnetic phase transition temperature (TL) in multiferroic Ni3V2O8 thin films. The simultaneous magnetic and ferroelectric transition in Ni3V2O8 exhibits a clear dielectric anomaly; we monitored TL under applied electric and magnetic fields using dielectric measurements. The transition temperature increases by 0.2 K±0.05 K when the sample is biased approximately 25 MV/m compared to zero bias. This electric-field control of the magnetic transition can be qualitatively understood using a mean-field model incorporating a tri-linear coupling between the magnetic order parameters and spontaneous polarization. The shape of the electric field-temperature phase boundary is consistent with the proper order parameter for the multiferroic phase in Ni3V2O8 being a linear combination of the magnetic and ferroelectric correlation functions.Publication van der Waals Interactions in Cholesteric Liquid Crystals(2000-03-01) Issaenko, Sergei A; Harris, A. BrooksMicroscopic calculations of the pitch of cholesteric liquid crystals are based on a few types of interactions between molecules: (1) short-range repulsive, (2) direct Coulomb, and (3) long-range van der Waals interactions. Recently, it was shown that first two types cannot be treated in the frame of mean-field approximation. Here we show that, contrary to common belief, an accurate evaluation of the intermolecular dispersion forces contributing to chiral ordering requires consideration of biaxial correlations between molecules which are neglected in the mean-field approximation. We found that in the presence of biaxial correlations chiral interactions depend very weakly on the anisotropy of the local (i.e., atomic) polarizability. Instead, the chiral interaction between two molecules is dominated by the character of biaxial correlations, the isotropic part of local polarizability of one molecule, and a chiral parameter of the other molecule, which characterizes the chiral molecular geometry and is similar to that found previously for steric interactions.Publication Location of the Ising Spin-Glass Multicritical Point on Nishimori's Line(1988-08-01) Le Doussal, Pierre; Harris, A. BrooksWe present arguments, based on local gauge invariance, that the multicritical point of Ising spin-glasses should be located on a particular line of the phase diagram known as Nishimori's line [tanh(βJ)=2p−1 for the ±J distribution]. One scaling axis is along the line, and the other is along the temperature direction. This scenario is generic for any random Ising model with a Nishimori line, in any number of dimensions, if the transitions are second order. The renormalization-group fixed point located inside Nishimori's manifold is expected to control multicriticality for a wider class of models.Publication Series Study of Random Animals in General Dimensions(1988-09-01) Adler, Joan; Meir, Yigal; Harris, A. Brooks; Aharony, Amnon; Duarté, José A. M. SWe construct general-dimension series for the random animal problem up to 15th order. These represent an improvement of five terms in four dimensions and above and one term in three dimensions. These series are analyzed, together with existing series in two dimensions, and series for the related Yang-Lee edge problem, to obtain accurate estimates of critical parameters, in particular, the correction to scaling exponent. There appears to be excellent agreement between the two models for both dominant and correction exponents.Publication Nature of the "Griffiths" Singularity in Dilute Magnets(1975-07-01) Harris, A. BrooksThe nature of the singular behavior pointed out by Griffiths for H=0 in dilute magnets is investigated. It is argued that for concentration p less than that for formation of an infinite cluster, all derivatives of M(H) are finite. The nonanalyticity in M(H) is due to a branch cut along the imaginary H axis having weight exp[−(const)/|H|] for |H|→0, and is thus too weak to be experimentally observable. Some numerical and exact analytic results for the dilute magnet on a Bethe lattice are presented.Publication ε Expansion for the Nishimori Multicritical Point of Spin Glasses(1989-11-01) Le Doussal, Pierre; Harris, A. BrooksThe renormalization-group recursion relations obtained by Chen and Lubensky for the multicritical point associated with simultaneous critical fluctuations in both the spin-glass and ferromagnetic order are reanalyzed. To first order in ε==6-d we find that the multicritical fixed point is located inside the Nishimori manifold and that the scaling axes agree with those obtained recently from general arguments. It is confirmed that the scaling along the Nishimori line and at the paramagnetic-spin-glass transition are related. We also point out some universal properties of the multicritical point of possible experimental interest.Publication Density of States of the Random-Hopping Model on a Cayley Tree(1985-06-01) Kim, Yup; Harris, A. BrooksWe formulate an integral equation and recursion relations for the configurationally averaged one-particle Green’s function of the random-hopping model on a Cayley tree of coordination number σ+1. This formalism is tested by applying it successfully to the nonrandom model. Using this scheme for 1≪σ<∞, we calculate the density of states of this model with a Gaussian distribution of hopping matrix elements in the energy range E2>Ec2, where Ec is a critical energy described below. The singularity in the Green’s function which occurs at energy E1(0) for σ=∞ is shifted to complex energy E1 (on the unphysical sheet of energy E) for small σ−1. This calculation shows that the density of states is a smooth function of energy E around the critical energy Ec=ReE1, in accord with Wegner’s theorem. In this formulation the density of states has no sharp phase transition on the real axis of E because E1 has developed an imaginary part. Using the Lifschitz argument, we calculate the density of states near the band edge for the model when the hopping matrix elements are governed by a bounded probability distribution. This case is also analyzed via a mapping similar to those used for dynamical systems, whereby the formation of energy band can be understood.Publication Recursive Enumeration of Clusters in General Dimension on Hypercubic Lattices(1987-08-15) Harris, A. Brooks; Meir, YigalA recursive method for enumerating clusters on a hypercubic lattice in d spatial dimensions is presented from which the weak embedding constants are determined as polynomials in d. A tabulation for all clusters having no free ends is available for nb≤15, where nb is the number of bonds. As illustrated here and elsewhere, this tabulation can be used to generate many series expansions. A novel method of checking the enumeration with an algebraic calculation is presented.Publication Series Study of a Spin-Glass Model in Continuous Dimensionality(1977-04-04) Fisch, Ronald; Harris, A. BrooksA high-temperature series expansion for the Edwards and Anderson spin-glass order-parameter susceptibility is computed for Ising spins on hypercubic lattices with nearest-neighbor interactions. The series is analyzed by Padé approximants with Rudnick-Nelson-type corrections to scaling. The results agree with the first-order ε expansion of Harris, Lubensky, and Chen. The critical exponent γQ increases monotonically with decreasing dimension, d, for d<6, and apparently tends to infinity at d=4; however, the critical temperature does not appear to go to zero at d=4.