Short‐distance monomer correlations in a self‐repelling polymer chain

We calculate the amplitude of the large‐wave vector scattering structure function S(q) of a long random coil in a good solvent, using field theory renormalization and expanding to first order in ϵ≡4‐ (dimension of space). This amplitude is some 35% smaller than that of a swollen Gaussian chain. This is consistent with nonrenormalization group theories and with experiment.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70497/2/JCPSA6-76-6-3300-1.pd

Spatial monomer distribution for a flexible polymer in a good solvent

We calculate the fourth moment 〈r4〉 of the average monomer–monomer separation in a flexible linear polymer in the excluded volume limit. The ratio 〈r4〉/〈r2〉2 is a universal number expressible in terms of the exponents γ and ν. The ratio is 8% smaller for the excluded volume chain than for the ideal chain. To account for the excluded volume interaction we use field theory methods to renormalize the Mayer–Fixman cluster expansion. Our approximation method of expanding in dimension of space minus four introduces an estimated uncertainty of 1%. The end point moment ratio 〈r4e〉/〈r2e〉2 behaves similarly.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71263/2/JCPSA6-74-4-2582-1.pd

Renormalized field theory of polymer solutions. I. Scaling laws

The large scale spatial correlations in a dilute solution of long chain molecules are dominated by excluded volume effects. We extend the field‐theoretic methods of Des Cloizeaux and De Gennes to describe these correlations. We derive general scaling laws which the experimentally measured correlation functions must obey. The dependence on (scattering) wave number, concentration, and chain length is thereby reduced to a function of two variables. This function may moreover be calculated via well‐studied approximations, leaving only an excluded volume parameter and a microscopic length parameter. Using the scaling law, we derive several experimentally observed power laws for parameters such as the radius of gyration, including limiting behavior for small overlap (independent chains), large overlap, and large wave vector.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70672/2/JCPSA6-66-5-2121-1.pd

The interpenetration of two chain polymers in a good solvent

The interpenetration of two excluded‐volume chain molecules of different size in dilute solution is studied via scaling and renormalization methods. The chains are found to interpenetrate much more strongly than smoothed‐density models suggest, in accordance with recent work by Khokhlov. The pair correlation funtion g(r) goes to zero at the origin only as a weak power of r. This power is related to Des Cloizeaux’s exponents ϑi describing intrachain correlations. The power is also related to the scaling exponents of star polymers. The mutual excluded volume MSL of two chains with greatly different length is proportional to the volume of the smaller chain and to the mass of the larger. Thus MSL is much smaller than a smoothed density model would predict. We discuss which chain correlations give rise to this small MSL. The universal coefficient relating MSL to the radius of gyration of the smaller chain is strongly dependent on the dimension d of space, according to our second‐order expansion in 4‐d. The interpenetration behavior predicted here affects measurable thermodynamic, scattering, and physical–chemical properties of the solution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70233/2/JCPSA6-77-8-4247-1.pd

Irreducible diagrams in Landau-Ginzburg field theory

It is shown that the free energy W of a Landau-Ginzburg-Wilson field theory with O(n) symmetry may be written in terms of the generating function V of diagrams irreducible in both propagator and interaction lines. This generalizes and simplifies a recent result of Des Cloizeaux. The functions W and V are related by a type of Legendre transformation on the bare mass variable.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24228/1/0000488.pd

Spin chain from membrane and the Neumann-Rosochatius integrable system

We find membrane configurations in AdS_4 x S^7, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS_5 x S^5. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.Comment: LaTeX, 16 pages, no figures; v2: 17 pages, title changed, explanations and references added; v3: more explanations added; v4: typos fixed, to appear in Phys. Rev.

Two critical ratios in polymer solutions

The interpenetration function Psi of a dilute solution of long randomly coiling molecules may be calculated by renormalisation group methods. This quantity is of special interest since it is entirely due to excluded volume effects. Two renormalisation methods give values for the excluded volume limit of Psi which are consistent with current experimental values. This indicates that the limiting value of Psi is easier to measure than previously thought. The experimental deviations from this limit can be well represented by a simple standard corrections-to-scaling formula. The authors also calculate the limiting ratio of average end-to-end distance to radius of gyration of these molecules. There is a small difference from the random chain value.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48796/2/jav11i9p1843.pd

Approximate degeneracies of zone boundary phonons in alkali halide crystals

We point out the existence of a pervasive pattern of near degeneracies of phonon frequencies in isobaric alkali halide crystals (NaBr, KCl, RbBr, CsI) which strongly suggests that their dynamical matrices are almost invariant under transformations which exchange positive and negative ions. We extend this hypothesis to a relation between phonon properties of "mirror" alkali halides in which the ions of one crystal are replaced by the oppositely charged isobaric ions of the other, such as RbCl and KBr. Experimental evidence supporting this can also be adduced. Similar near degeneracies universally occurring in NaCl structure alkali halides and alkaline earth oxides are also noted and a possible dynamical basis for understanding these suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24456/1/0000730.pd

Wess-Zumino Terms in Supersymmetric Gauge Theories

The Wess-Zumino term is constructed for supersymmetric QCD with two colors and flavors, and is shown to correctly reproduce the anomalous Ward identities. Supersymmetric QCD is also shown not to have topologically stable skyrmion solutions because of baryon flat directions, which allow them to unwind. The generalization of these results to other supersymmetric theories with quantum modified constraints is discussed.Comment: 4 pages (revtex

Optimal real-space renormalisation

Using a continuous class of real-space renormalisation transformations the authors study the critical behaviour of the Ising model in a variety of two-dimensional lattices. They use the simplest possible cluster, with two cells, and a single renormalised coupling. Certain of these transformations-well separated from the majority spin rule-produce sharply more accurate critical properties than the rest. From this study they note an optimal set of conditions which characterise the successful transformations. The optimal transformations appear to have a certain 'locality' property: renormalised couplings beyond nearest neighbour are especially small.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48799/2/jav14i2p447.pd