Derivation of effective spin models from a three band model for CuO_2-planes

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO_2-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La_2CuO_4. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping t_pd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Pade approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Pade approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized.Comment: 27 pages, 10 figures. Changed from particle to hole notation, right value for the charge transfer gap used; this results in some changes in the figures and a higher value of the ring exchang

Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension

The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d=6,7 which are larger or equal to the assumed upper critical dimension, d_u=6, mean-field behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.Comment: 8 pages and 13 figures; A consise summary of this work can be found in the papercore database at http://www.papercore.org/Ahrens201

Large-deviation properties of the extended Moran model

The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model (alpha->0) as well as the uniform distribution (alpha=1). Using a statistical mechanics-based large-deviation approach, the distributions can be studied over an extended range of the support, down to probabilities like 10^{-70}, which allowed us to study the change of the tails of the distribution when varying the value of alpha in [0,2]. We find exponential distributions p(t_mrca)~ delta^{t_mrca} in all cases, with systematically varying values for the base delta. Only for the cases alpha=0 and alpha=1, analytical results are known, i.e., delta=\exp(-2/N^2) and delta=2/3, respectively. We recover these values, confirming the validity of our approach. Finally, we also study the correlations between t_mrca and the number of descendants.Comment: 8 pages, 8 figure

The long and winding road: Routine creation and replication in multi-site organizations

Prior research on organizational routines in the ‘capabilities’ literature has either studied how new routines are created during an exploratory process of variation and selection or how existing routines are replicated during a phase of exploitation. Few studies have analyzed the life cycle of new routine creation and replication as an integrated process. In an in-depth case study of England’s Highways Agency, this paper shows that the creation and replication of a new routine across multiple sites involves four sequential steps: envisioning, experimenting, entrenching and enacting. We contribute to the capabilities research in two ways: first, by showing how different organizational levels, capabilities and logics (cognitive and behavioural) shape the development of new routines; and second, by identifying how distinct evolutionary cycles of variation and selective retention occur during each step in the process. In contrast with prior research on replication as an exact copy of a template or existing routine, our study focuses on the replication of an entirely new routine (based on novel principles) that is adapted to fit local operational conditions during its large-scale replication across multiple sites. We draw upon insights from adjacent ‘practice research’ and suggest how capabilities and practice studies may complement each other in future research on the evolution of routines