Quantum Phase Transition from a Spin-liquid State to a Spin-glass State in the Quasi-1D Spin-1 System Sr1-xCaxNi2V2O8

We report a quantum phase transition from a spin-liquid state to a spin-glass state in the quasi-one dimensional (1D) spin-1 system Sr1-xCaxNi2V2O8, induced by a small amount of Ca-substitution at Sr site. The ground state of the parent compound (x = 0) is found to be a spin-liquid type with a finite energy gap of 26.6 K between singlet ground state and triplet excited state. Both dc-magnetization and ac-susceptibility studies on the highest Ca-substituted compound (x = 0.05) indicate a spin-glass type magnetic ground state. With increasing Ca-concentration, the spin-glass ordering temperature increases from 4.5 K (for the x = 0.015 compound) to 6.25 K (for the x = 0.05 compound). The observed results are discussed in the light of the earlier experimental reports and the theoretical predictions for a quasi-1D spin-1 system.Comment: 26 pages, 8 figures, 3 table

Dynamics of weakly coupled random antiferromagnetic quantum spin chains

We study the low-energy collective excitations and dynamical response functions of weakly coupled random antiferromagnetic spin-1/2 chains. The interchain coupling leads to Neel order at low temperatures. We use the real-space renormalization group technique to tackle the intrachain couplings and treat the interchain couplings within the Random Phase Approximation (RPA). We show that the system supports collective spin wave excitations, and calculate the spin wave velocity and spectra weight within RPA. Comparisons will be made with inelastic neutron scattering experiments quasi-one-dimensional disordered spin systems such as doped CuGeO$_3$Comment: 4 page

On representations of Clifford algebras of ternary cubic forms

In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$. We study general properties of Ulrich bundles, and using a recent classification of Casanellas and Hartshorne, deduce the existence of irreducible representations of $C_f$ of every possible dimension.Comment: 9 pages, to appear in proceedings for the conference "New Trends in Noncommutative Algebra: A Conference in Honor of Ken Goodearl's 65th Birthday

Pfaffian quartic surfaces and representations of Clifford algebras

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized Clifford algebra $C_f$ associated to $f$ and Ulrich bundles on the surface $X_f:=\{w^{4}=f(x_1,x_2,x_3)\} \subseteq \mathbb{P}^3$ to construct a positive-dimensional family of irreducible representations of $C_f.$ The main part of our construction, which is of independent interest, uses recent work of Aprodu-Farkas on Green's Conjecture together with a result of Basili on complete intersection curves in $\mathbb{P}^{3}$ to produce simple Ulrich bundles of rank 2 on a smooth quartic surface $X \subseteq \mathbb{P}^3$ with determinant $\mathcal{O}_X(3).$ This implies that every smooth quartic surface in $\mathbb{P}^3$ is the zerolocus of a linear Pfaffian, strengthening a result of Beauville-Schreyer on general quartic surfaces.Comment: This paper contains a proof of the main result claimed in the erroneous preprint arXiv:1103.0529. We also extend this result to all smooth quartic surface

Magnetocaloric effect and critical behavior near the paramagnetic to ferrimagnetic phase transition temperature in TbCo2-xFex

Magnetocaloric effect (MCE) in TbCo2-xFex has been studied by dc magnetization measurements.On substituting Fe in TbCo2, not only the magnetic transition temperature is tuned to room temperature, but also the operating temperature range for MCE is increased from 50 K for TbCo2 to 95 K for TbCo1.9Fe0.1. The maximum magnetic entropy change (-{\Delta}SM) for TbCo1.9Fe0.1 is found to be 3.7 J kg-1 K-1 for a 5 T field change, making it a promising candidate for magnetic refrigeration near room temperature. The temperature dependent neutron diffraction study shows a structural phase transition (from cubic to rhombohedral phase with lowering of temperature) which is associated with the magnetic phase transition and these transitions broaden on Fe substitution. To investigate the nature of the paramagnetic to ferrimagnetic phase transition, we performed a critical exponent study. From the derived values of critical exponents, we conclude that TbCo2 belongs to the 3D Heisenberg class with short-range interaction, while on Fe substitution it tends towards mean-field with long-range interaction. The derived values of critical exponents represent the phenomenological universal curve for the field dependence of {\Delta}SM, indicating that TbCo2 and TbCo1.9Fe0.1 belong to two different universality classes.Comment: 12 figure

A secure data outsourcing scheme based on Asmuth – Bloom secret sharing

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Data outsourcing is an emerging paradigm for data management in which a database is provided as a service by third-party service providers. One of the major benefits of offering database as a service is to provide organisations, which are unable to purchase expensive hardware and software to host their databases, with efficient data storage accessible online at a cheap rate. Despite that, several issues of data confidentiality, integrity, availability and efficient indexing of users’ queries at the server side have to be addressed in the data outsourcing paradigm. Service providers have to guarantee that their clients’ data are secured against internal (insider) and external attacks. This paper briefly analyses the existing indexing schemes in data outsourcing and highlights their advantages and disadvantages. Then, this paper proposes a secure data outsourcing scheme based on Asmuth–Bloom secret sharing which tries to address the issues in data outsourcing such as data confidentiality, availability and order preservation for efficient indexing