Critical behavior of an Ising model with aperiodic interactions

We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, the uniform fixed point in the parameter space becomes fully unstable. We analyze some limiting cases, and propose a heuristic criterion to check the relevance of the fluctuations.Comment: latex file, 5 figures, accepted by Braz. Jour. Phy

Persistence in Corporate Networks

We examine the bipartite graphs of German corporate boards in 1993, 1999 and 2005, and identify cores of directors who are highly central in the entire network while being densely connected among themselves. The novel feature of this paper is the focus on the dynamics of these networks. Germany's corporate governance has experienced significant changes during this time, and there is substantial turnover in the identity of core members, yet we observe the persistent presence of a network core, which is even robust to changes in the tail distribution of multiple board memberships. Anecdotal evidence suggests that core persistence originates from the board appointment decisions of largely capitalized corporations

Charged spin 1/2 particle in an arbitrary magnetic field in two spatial dimensions: a supersymmetric quantum mechanical system

It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator of a nilpotent operator and its hermitian conjugate. Consequently, the Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra can then be exploited to explicitly construct the exact zero energy ground state wavefunction for the system. Modulo this ground state, the remainder of the eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs. We also construct the spatially asymptotic form of the magnetic field which produces a finite magnetic flux and associated zero energy normalizable ground state wavefunction.Comment: 10 pages, LaTe