Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Thermal Transport and Strong Mass Renormalization in NiCl(2)-4SC(NH(2))(2)

Several quantum paramagnets exhibit magnetic-field-induced quantum phase transitions to an anti-ferromagnetic state that exists for H(c1) <= H <= H(c2). For some of these compounds, there is a significant asymmetry between the low-and high-field transitions. We present specific heat and thermal conductivity measurements in NiCl(2)-4SC(NH(2))(2), together with calculations which show that the asymmetry is caused by a strong mass renormalization due to quantum fluctuations for H <= H(c1) that are absent for H >= H(c2). We argue that the enigmatic lack of asymmetry in thermal conductivity is due to a concomitant renormalization of the impurity scattering.

Anomalous lattice parameter of magnetic semiconductor alloys

The addition of transition metals to III-V semiconductors radically changes their electronic, magnetic, and structural properties. We show by ab initio calculations that in contrast to the conventional semiconductor alloys, the lattice parameter in magnetic semiconductor alloys, including those with diluted concentration, strongly deviates from Vegard's law. We find a direct correlation between the magnetic moment and the anion-transition metal bond lengths and derive a simple and general formula that determines the lattice parameter of a particular magnetic semiconductor by considering both the composition and magnetic moment. This dependence can explain some experimentally observed anomalies and stimulate other kind of investigations.

Magnetic resonant x-ray diffraction study of europium telluride

Here we use magnetic resonant x-ray diffraction to study the magnetic order in a 1.5 mu m EuTe film grown on (111) BaF(2) by molecular-beam epitaxy. At Eu L(II) and L(III) absorption edges, a resonant enhancement of more than two orders was observed for the sigma ->pi(') diffracted intensity at half-order reciprocal-lattice points, consistent with the magnetic character of the scattering. We studied the evolution of the (1/21/21/2) magnetic reflection with temperature. When heating toward the Neel temperature (T(N)), the integrated intensity decreased monotonously and showed no hysteresis upon cooling again, indicating a second-order phase transition. A power-law fit to the magnetization versus temperature curve yielded T(N)=9.99(1) K and a critical exponent beta=0.36(1), which agrees with the renormalization theory results for three-dimensional Heisenberg magnets. The fits to the sublattice magnetization dependence with temperature, disregarding and considering fourth-order exchange interactions, evidenced the importance of the latter for a correct description of magnetism in EuTe. A value of 0.009 was found for the (2j(1)+j(2))/J(2) ratio between the Heisenberg J(2) and fourth-order j(1,2) exchange constants. The magnetization curve exhibited a round-shaped region just near T(N) accompanied by an increase in the magnetic peak width, which was attributed to critical scattering above T(N). The comparison of the intensity ratio between the (1/21/21/2) and the (1/21/21/2) magnetic reflections proved that the Eu(2+) spins align within the (111) planes, and the azimuthal dependence of the (1/21/21/2) magnetic peak is consistent with the model of equally populated S domains.

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3509374]

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice. Different regimes for transmission of a broad and a narrow solitons are investigated. Reflections and transmissions of solitons are predicted as a function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials.

Magnetoelastic and thermal effects in the BiMn(2)O(5) lattice: A high-resolution x-ray diffraction study

High-resolution synchrotron x-ray diffraction measurements were performed on single crystalline and powder samples of BiMn(2)O(5). A linear temperature dependence of the unit cell volume was found between T(N)=38 and 100 K, suggesting that a low-energy lattice excitation may be responsible for the lattice expansion in this temperature range. Between T(*)similar to 65 K and T(N), all lattice parameters showed incipient magnetoelastic effects, due to short-range spin correlations. An anisotropic strain along the a direction was also observed below T(*). Below T(N), a relatively large contraction of the a parameter following the square of the average sublattice magnetization of Mn was found, indicating that a second-order spin Hamiltonian accounts for the magnetic interactions along this direction. On the other hand, the more complex behaviors found for b and c suggest additional magnetic transitions below T(N) and perhaps higher-order terms in the spin Hamiltonian. Polycrystalline samples grown by distinct routes and with nearly homogeneous crystal structure above T(N) presented structural phase coexistence below T(N), indicating a close competition amongst distinct magnetostructural states in this compound.

Precise determination of quantum critical points by the violation of the entropic area law

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two-dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so-called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and noncritical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.