A differential cluster variation method for analysis of spiniodal decomposition in alloys

A differential cluster variation method (DCVM) is proposed for analysis of spinoidal decomposition in alloys. In this method, lattice symmetry operations in the presence of an infinitesimal composition gradient are utilized to deduce the connection equations for the correlation functions and to reduce the number of independent variables in the cluster variation analysis. Application of the method is made to calculate the gradient energy coefficient in the Cahn-Hilliard free energy function and the fastest growing wavelength for spinodal decomposition in Al-Li alloys. It is shown that the gradient coefficient of congruently ordered Al-Li alloys is much larger than that of the disordered system. In such an alloy system, the calculated fastest growing wavelength is approximately 10 nm, which is an order of magnitude larger than the experimentally observed domain size. This may provide a theoretical explanation why spinodal decomposition after a congruent ordering is dominated by the antiphase boundaries.Comment: 15 pages, 7 figure

Influence of Coulomb interaction on the anisotropic Dirac cone in graphene

Anisotropic Dirac cones can appear in a number of correlated electron systems, such as cuprate superconductors and deformed graphene. We study the influence of long-range Coulomb interaction on the physical properties of an anisotropic graphene by using the renormalization group method and 1/N expansion, where N is the flavor of Dirac fermions. Our explicit calculations reveal that the anisotropic fermion velocities flow monotonously to an isotropic fixed point in the lowest energy limit in clean graphene. We then incorporate three sorts of disorders, including random chemical potential, random gauge potential, and random mass, and show that the interplay of Coulomb interaction and disorders can lead to rich and unusual behaviors. In the presence of strong Coulomb interaction and a random chemical potential, the fermion velocities are driven to vanish at low energies and the system turns out to be an exotic anisotropic insulator. In the presence of Coulomb interaction and other two types of disorders, the system flows to an isotropic low-energy fixed point more rapidly than the clean case, and exhibits non-Fermi liquid behaviors. We also investigate the nonperturbative effects of Coulomb interaction, focusing on how the dynamical gap is affected by the velocity anisotropy. It is found that the dynamical gap is enhanced (suppressed) as the fermion velocities decrease (increase), but is suppressed as the velocity anisotropy increases.Comment: 24 pages, 17 figure