Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon

We present a detailed analysis of the Kitaev--Heisenberg model on a single hexagon. The energy spectra and spin--spin correlations obtained using exact diagonalisation indicate quantum phase transitions between antiferromagnetic and anisotropic spin correlations when the Kitaev interactions increase. In cluster mean-field approach frustrated nearest neighbor exchange stabilizes the stripe phase in between the N\'eel phase and frustrated one which evolves towards the Kitaev spin liquid.Comment: 3 pages, 3 figures, Euroconference Physics of Magnetism, Pozna\'n 201

Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems

Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The Gramian is generalized and steering functions between memory values are characterized.Comment: Submitted 30/Nov/2009; Revised (major revision) 24/April/2010; Accepted (after minor revision) 22/July/2010; for publication in Signal Processin