Four Dimensional Graphene

Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H_4. We first study the link between the H_4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5) satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots \alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal lattice H_4^\ast. It is shown, amongst others, that these zeros live at the sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2) \gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector. Other features such as differences with BBTW model as well as the link between the Dirac operator following from our construction and the one suggested by Creutz using quaternions, are also given. Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.Comment: LaTex, 26 pages, 1 figure, To appear in Phys Rev

Monte Carlo simulation of magnetic phase transitions in Mn doped ZnO

The magnetic properties of Mn-doped ZnO semi-conductor have been investigated using the Monte Carlo method within the Ising model. The temperature dependences of the spontaneous magnetization, specific heat and magnetic susceptibility have been constructed for different concentrations of magnetic dopant Mn and different carrier concentrations. The exact values of Mn concentration and carrier concentration at which high temperature transition occurs are determined. An alternative for the explanation of some controversies concerning the existence and the nature of magnetism in Mn diluted in ZnO systems is given. Other features are also studied.Comment: 10 pages, 9 figures, To appear in Journal of Magnetism and Magnetic Material