On the phase diagram of the anisotropic XY chain in transverse magnetic field

We investigate an explicite formula for ground state energy of the anisotropic XY chain in transverse magnetic field. In particular, we examine the smoothness properties of the expression, given in terms of elliptic integrals. We confirm known 2d-Ising type behaviour in the neighbourhood of certain lines of phase diagram and give more detailed information there, calculating a few next-to-leading exponents as well as corresponding amplitudes. We also explicitly demonstrate that the ground-state energy is infinitely differentiable on the boundary between ferromagnetic and oscillatory phases.Comment: 15 pages, 8 figure

Inequalities between ground-state energies of Heisenberg models

The Lieb-Schupp inequality is the inequality between ground state en- ergies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture

Increasing Stretchability of Conjugated Polymers Using Metal-Ligand Coordination

Stretchable and mechanically robust materials are now becoming crucial for the development of wearable electronics. In particular, semiconducting conjugated polymers have been shown to be remarkable candidates when preparing new electronic devices as the exhibit good charge transport properties, synthetic versatility and easy tunability. In recent years, the development of these types of materials have been utilized the use of dynamic crosslinking, especially metal-ligand interactions, is a promising avenue to prepare and design stretchable materials while also enabling novel properties such as self-healing. However, in their synthesis and application, there are many challenges overcome to achieve stretchable conjugated polymers, due to the intrinsic competition between electronic and mechanical properties. The objective of the project is to develop a novel strategy towards developing intrinsically stretchable and self-healing conjugated polymers for application in stretchable electronics. This main objective will be achieved by incorporating metal coordinating moieties, namely imine side-chains, to the polymer in order to chelate to Iron(II). This dynamic coordination will allow for the polymer network to dissipate strain, thus enhancing the mechanical properties of the materials. Moreover, this will also allow for regeneration of the polymer network after being damaged through a process known as self-healing. This presentation will discuss our recent progress toward new metal-coordinating conjugated polymers, especially focusing on their design and preparation

Some properties of frustrated spin systems: extensions and applications of Lieb-Schupp approach

Lieb and Schupp have obtained, using certain version of ``spin-reflection positivity'' method, a number of ground-state properties for frustrated Heisenberg models. One group of these results is related to singlet nature of ground state and it needs an assumption of reflection symmetry present in the system. In this paper, it is shown that the result holds also for other symmetries (inversion etc.). The second Lieb-Schupp result is relation between ground-state energies of certain systems. In the paper, this relation is applied to multidimensional models on various lattices.Comment: 15 pages, 8 eps figures, revtex