THE EFFECT OF CORTICO-THALAMIC CONNECTIONS ON THE DIVERSITY OF CORTICAL ACTIVATIONS AS MODELED BY THE ISING MODEL

The influence of the thalamus on the diversity of cortical activations is investigated in terms of the Ising model with respect to progressive levels of cortico-thalamic connectivity. The results show that better diversity is achieved at lower modulation levels, being higher than those obtained with counterpart network models.

Extending the use of canonical and microcanonical Monte Carlo algorithms to spin models

We describe the canonical and microcanonical Monte Carlo algorithms for different systems that can be described by spin models. Sites of the lattice, chosen at random, interchange their spin values, provided they are different. The canonical ensemble is generated by performing exchanges according to the Metropolis prescription whereas in the microcanonical ensemble, exchanges are performed as long as the total energy remains constant. A systematic finite size analysis of intensive quantities and a comparison with results obtained from distinct ensembles are performed and the quality of results reveal that the present approach may be an useful tool for the study of phase transitions, specially first-order transitions. (C) 2009 Elsevier B.V. All rights reserved.

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Antiferromagnetic spherical spin-glass model

We study the thermodynamic properties and the phase diagrams of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. It is a two-sublattice version of the ferromagnetic spherical p-spin glass model. We consider both the replica-symmetric and the one-step replica-symmetry-breaking solutions, the latter being the most general solution for this model. We find paramagnetic, spin-glass, antiferromagnetic and mixed or glassy antiferromagnetic phases. The phase transitions are always of second order in the thermodynamic sense, but the spin-glass order parameter may undergo a discontinuous change.

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.

Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

Influence of super-ohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics. Copyright (C) EPLA, 2011

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows LIS to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other. (C) 2009 Elsevier B.V. All rights reserved.