Properties of sulfonated polysulfone ionomers.

The structure-property relationships of sulfonated polysulfone ionomers were investigated. The techniques of Fourier Transform Infrared, Differential Scanning Calorimetry, Dynamic-Mechanical Analysis, Small Angle X-ray Scattering and Water Absorption were used to provide Information on the nature of ionic interactions 1n these Ionomers. From these structure-property studies, the ionomeric structure is best described as consisting largely of ionic multiplets composed of ion pairs, quartets, etc

Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field

The anisotropic s=1/2 anti-ferromagnetic Heisenberg chain in the presence of an external magnetic field is studied by using the standard quantum renormalization group. We obtain the critical line of the transition from partially magnetized (PM) phase to the saturated ferromagnetic (SFM) phase. The crossover exponent between the PM phase and anti-ferromagnetic Ising (AFI) phase is evaluated. Our results show that the anisotropy(\d) term is relevant and causes crossover. These results indicate that the standard RG approach yields fairly good values for the critical points and their exponents. The magnetization curve, correlation functions and the ground state energy per site are obtained and compared with the known exact results.Comment: A LaTex file(20 pages) and 9 PS figure

Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions

We have extended the application of quantum renormalisation group (QRG) to the anisotropic Heisenberg model with next-nearest neighbour (n-n-n) interaction. The second order correction has to be taken into account to get a self similar renormalized Hamiltonian in the presence of n-n-n-interaction. We have obtained the phase diagram of this model which consists of three different phases, i.e, spin-fluid, dimerised and Ne'el types which merge at the tri-critical point. The anisotropy of the n-n-n-term changes the phase diagram significantly. It has a dominant role in the Ne'el-dimer phase boundary. The staggered magnetisation as an order parameter defines the border between fluid-Ne'el and Ne'el-dimer phases. The improvement of the second order RG corrections on the ground state energy of the Heisenberg model is presented. Moreover, the application of second order QRG on the spin lattice model has been discussed generally. Our scheme shows that higher order corrections lead to an effective Hamiltonian with infinite range of interactions.Comment: 10 pages, 4 figures and 1 tabl

Specific heat of the quantum Heisenberg antiferromagnet by a renormalization-group approach

The finite-temperature renormalization scheme has been applied to the antiferromagnetic Heisenberg model on the triangular lattice with inhomogeneous bonds (with the kagome lattice as a limiting case). In order to preserve the isotropy of the Hamiltonian, this method was modified by using the eigenvectors of the so-called ''parity'' operator. This allows to analyze the model which corresponds to some experiments of a He-3 layer adsorbed on graphite in the mK temperature region. The appearence of more than one maximum in the specific heat is discussed as a function of the imposed inhomogeneity.status: publishe

Renormalization of the anisotropic linear xy model

The renormalization scheme recently proposed by White is applied to the d = 1 anisotropic XY model in a transverse field (AXY). It is found that this scheme offers a distinct improvement over standard techniques as far as the computation of the ground state is concerned. However, compared to the Ising model in a transverse field, on account of more complicated symmetries the AXY demands more precautions during the construction of a renormalization-group transformation. The new method predicts definitely better the location of the phase transition in the XY-like region than in the Ising-like region, but only in the Ising-like region is there any progress for the critical exponent alpha.status: publishe

A new renormalization approach to the ground state of the anisotropic XY model

The renormalization scheme recently proposed by White is applied to the d=1 anisotropic XY model in a transverse field (AXY). A flow diagram, critical exponents and energies have been calculated. It is found that this scheme is a distinct improvement over the standard technique as far as the computation of the ground state is concerned. The accuracy increases rapidly, when we keep more states in each renormalization step, but the errors in the ground state energy are always the largest in the neighborhood of the phase transitions. Comparing with the Ising model in a transverse field, on account of more complicated symmetries, the AXY demands more precautions during constructing a renormalization group transformation.status: publishe