Exact results for the adsorption of a semiflexible copolymer chain in three dimensions

Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular to the preferred direction of the walk of the copolymer chain in three dimensions. The stiffness of the chain has been accounted by introducing an energy barrier for each bend in the walk of the copolymer chain. Exact value of adsorption desorption transition points have been determined using generating function method for the cases in which one type of monomer is having interaction with the surface viz., (i) no interaction (ii) attractive interaction and (iii) repulsive interaction. Results obtained in each of the case show that for stiffer copolymer chain adsorption transition occurs at a smaller value of monomer surface attraction than a flexible copolymer chain. These features are similar to that of a semi-flexible homopolymer chain adsorption.Comment: 8 pages with one figur

Random Walks with Long-Range Self-Repulsion on Proper Time

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included) IFUP-Th 13/92 and SNS 14/9

Interplay between field-induced and frustration-induced quantum criticalities in the frustrated two-leg Heisenberg ladder

The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan-Wigner transformation in dimensions higher than one and bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities in this system. The present work could constitute a prototype for those systems showing multiple, perhaps sometimes competing, quantum criticalities. We calculate several physical quantities like the magnetization and spin susceptibility as functions of field and temperature.Comment: 9 pages, 8 figures, submitted to the Canadian Journal of Physic

The competition of hydrogen-like and isotropic interactions on polymer collapse

We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction strengths are all the same then the classical $\theta$-point collapse transition occurs on lowering the temperature, and the polymer enters the isotropic liquid-drop phase known as the collapsed globule. On the other hand, strongly favouring the hydrogen-like interactions give rise to an anisotropic folded (solid-like) phase on lowering the temperature. We use Monte Carlo simulations up to a length of 256 to map out the phase diagram in the plane of parameters and determine the order of the associated phase transitions. We discuss the connections to semi-flexible polymers and other polymer models. Importantly, we demonstrate that for a range of energy parameters two phase transitions occur on lowering the temperature, the second being a transition from the globule state to the crystal state. We argue from our data that this globule-to-crystal transition is continuous in two dimensions in accord with field-theory arguments concerning Hamiltonian walks, but is first order in three dimensions

Force-induced desorption of a linear polymer chain adsorbed on an attractive surface

We consider a model of self-avoiding walk on a lattice with on-site repulsion and an attraction for every vertex of the walk visited on the surface to study force-induced desorption of a linear polymer chain adsorbed on an attractive surface and use the exact enumeration technique for analyzing how the critical force for desorption $f_c(T)$ depends on the temperature. The curve $f_c(T)$ gives the boundary separating the adsorbed phase from the desorbed phase. Our results show that in two dimensions where surface is a line the force $f_c(T)$ increases monotonically as temperature is lowered and becomes almost constant at very low temperatures. In case of three-dimensions we, however, find re-entrance, i. e. $f_c(T)$ goes through a maximum as temperature is lowered. The behaviour of the polymer chain at different values of temperature and force is examined by calculating the probability distribution of the height from the surface of the vertex at which external force is applied.Comment: Preprint 15 pages with 8figures and two tables. The file table-2d.ps and table-3d.ps lists C_N(Ns,h) for given N with all possible Ns and h in two and three dimension

Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain

Highly accurate results are presented for the susceptibility, $\chi (T)$ of the $s=1/2$ Heisenberg antiferromagnetic chain for all temperatures, using the Bethe ansatz and field theory methods. After going through a rounded peak, $\chi (T)$ approaches its asympotic zero-temperature value with infinite slope.Comment: 8 pages and 3 postscript figures appended (uuencoded), Revtex, Report #:UBCTP-94-00

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Molecular observation of contour-length fluctuations limiting topological confinement in polymer melts

In order to study the mechanisms limiting the topological chain confinement in polymer melts, we have performed neutron-spin-echo investigations of the single-chain dynamic-structure factor from polyethylene melts over a large range of chain lengths. While at high molecular weight the reptation model is corroborated, a systematic loosening of the confinement with decreasing chain length is found. The dynamic-structure factors are quantitatively described by the effect of contour-length fluctuations on the confining tube, establishing this mechanism on a molecular level in space and time

Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder

The ground state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean field theory and the density matrix renormalization group. Spin wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, $J_\perp$, in the ladder. It is found that the gap is linear in $J_\perp$ for $J_\perp\gg 1$ and goes to zero for $J_\perp\to 0$. The mean field theory agrees well with the numerical results.Comment: 11pages,6 figures (upon request) Revtex 3.0, Report#CRPS-94-0