Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model

The effect of different initial values m₀ of magnetization and structural defects on the nonequilibrium critical behavior of the 3D Ising model have been analyzed numerically using the Monte Carlo method. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility has revealed a substantial influence of the initial states on the aging effects that are characterized by anomalous retardation of relaxation and correlation in the system upon an increase in the waiting time. We have studied the violations of the fluctuation–dissipation theorem and calculated the limiting fluctuation–dissipation ratio. It is shown that in the nonequilibrium critical behavior of the 3D Ising model, two universality subclasses corresponding to the evolution of the system from the high-temperature (with m₀ = 0) and low-temperature (with m₀ = 1) initial states with the values of the limiting fluctuation–dissipation ratio typical of these states can be singled out.     

Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.     

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m₀ and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m₀ These subclasses correspond to the system evolution from the high-temperature (m₀ = 0) and low-temperature (m₀ = 1) initial states with limit FDRs characteristic of these states.     

Revisiting the nonequilibrium phase transition of the triplet-creation model

The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition becomes discontinuous. As the diffusion probability increases the critical exponents change continuously from the ordinary directed percolation (DP) class to the compact directed percolation (CDP). The fractal dimension of the critical cluster, however, switches abruptly between those two universality classes. Strong crossover effects in both methods make it difficult, if not impossible, to establish the exact location of the tricritical point.     

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

A Monte Carlo study of the specific features of the nonequilibrium critical behavior has been performed for the two-dimensional “pure” and structurally disordered Ising models in the course of their evolution from the low-temperature initial state at spin concentrations p = 1.0, 0.9, and 0.8. It is shown for the first time that the pinning of domain walls by structural defects leads to the anomalously strong slowing down in the evolution of the autocorrelation function characterized by the superaging effect with exponents μ = 6.25(5) and μ = 6.75(5) for the model with the spin concentrations p = 0.9 and 0.8, respectively. The pure model exhibits the conventional aging with the exponent μ = 1. It is found that the superaging effects in structurally disordered systems lead to vanishing of the limiting fluctuation?dissipation ratio X^∞, whereas X^∞ = 0.751(24) for the pure model.     

RIBs in-flight production at the Laboratori Nazionali del Sud

Microscopic modeling of complex systems by cellular automata, which deal with particles at lattice sites interacting via simple local rules, involves some arbitrariness besides a drastic simplification of nature. Here we briefly report on some recent work on the influence of dynamic details on the morphological and critical properties of one of such model systems. In particular, we discuss on the similarities and differences between a kinetic nonequilibrium Ising model—which is a prototype for nonequilibrium anisotropic phase transitions—and its off–lattice counterpart, namely, an analogue in which the spatial coordinates of the particles vary continuously. We also pay attention to a related driven lattice model with nearest-neighbor exclusion.     

Critical behavior of a dynamical percolation model

The critical behavior of the dynamical percolation model, which realizes the molecular-aggregation conception and describes the crossover between the hadronic phase and the partonic phase, is studied in detail. The critical percolation distance for this model is obtained by using the probability P∞ of the appearance of an infinite cluster. Utilizing the finite-size scaling method the critical exponents γ/v and T are extracted from the distribution of the average cluster size and cluster number density. The influences of two model related factors, I.e. The maximum bond number and the definition of the infinite cluster, on the critical behavior are found to be small.     

Dependency of percolation critical exponents on the exponent of power law size distribution

The standard percolation theory uses objects of the same size. Moreover, it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently, the universality of the percolation theory is still valid. In this study, the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated. Two different object shapes i.e., stick-shaped and square are considered. These two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs. The finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent. In particular, the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically. As a result, this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution.     

Strong disorder fixed point in absorbing-state phase transitions

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.     

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.     

Symmetry of the Unsteady Linearized Boltzmann Equation in a Fixed Bounded Domain

A symmetric relation between time-dependent problems described by the linearized Boltzmann equation is obtained for a gas in a fixed bounded domain. General representations of the total mass, momentum, and energy in the domain, as well as their fluxes through the boundary, in terms of an appropriate Green function are derived from that relation. Several application examples are presented. Similarities to the fluctuation–dissipation theorem in the linear response theory and its generalization to gas systems of arbitrary Knudsen numbers are also discussed. The present paper is an extension of the previous work of the author (Takata in J. Stat. Phys. 136: 751–784, 2009) to time-dependent problems.     

New Universality Class Associated with Jahn–Teller Distortion and Double Exchange

The scaling of the magnetic heat capacity in the two manganites La0.85Ag0.15MnO3 and Sm0.55Sr0.45MnO has given the critical exponents α = –0.23 and ν = 0.7433 of the heat capacity and correlation radius of the magnetic order parameter, respectively, which do not belong to any known universality class. These results cannot be attributed to chemical inhomogeneities and/or structural imperfections because the samples are of a high quality. Thus, unusual critical exponents can be associated not only with the chemical disorder and/or structural defects but also with the collective behavior of the lattice. An analogy has been revealed between the effects of the magnetic field and doping on ternary oxides of transition metals: the magnetic field affecting lattice distortions through the orientation of t2g orbitals acts as chemical doping. It seems that scaling relations are more stable than critical exponents in them. The synchronism of lattice distortions and ferromagnetism leads to a novel criticality, but their desynchronization induced by magnetostructural disorder results in the violation of scaling relations between isothermal and isomagnetic exponents. Although double-exchange systems demonstrate novel criticality, they satisfy scaling relations until the magnetic behavior is synchronized with the coherent lattice behavior in the form of cooperative Jahn–Teller distortions. Breaking of double exchange bonds leads to the formation of metamagnetic clusters with magnetic dipole–dipole interaction between them, which desynchronizes lattice distortions and ferromagnetism, resulting in the violation of scaling relations. The proposed new universality class includes diverse materials such as manganites, cobaltites, crystalline Fe–Pt and amorphous Fe–Mn alloys, and high-Tc superconductors. Unusual criticality in double-exchange systems is due to an unusual semiclassical nature of double-exchange ferromagnetism caused by real exchange, i.e., electron current through Mn3+–O–Mn4+ chains with the conservation of the spin rather than by virtual exchange as in a usual ferromagnet. Double-exchange ferromagnetism arises only because to freely itinerate, electrons orient the magnetic moments of Mn cations in a single direction.     

Directed percolation criticality in turbulent liquid crystals

We experimentally investigate the critical behavior of a phase transition between two topologically different turbulent states of electrohydrodynamic convection in nematic liquid crystals. The statistical properties of the observed spatiotemporal intermittency regimes are carefully determined, yielding a complete set of static critical exponents in full agreement with those defining the directed percolation class in 2+1 dimensions. This constitutes the first clear and comprehensive experimental evidence of an absorbing phase transition in this prominent nonequilibrium universality class.     

Nonequilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d(c)=4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A-->A+A, A+A-->A, and A-->0. We study a hierarchy of such DP processes for particle species A,B,..., unidirectionally coupled via the reactions A-->B, ...(with rates mu(AB),...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents beta(i) which are markedly reduced at each hierarchy level i> or =2. This scenario can be understood on the basis of the mean-field rate equations, which yield beta(i)=1/2(i-1) at the multicritical point. Using field-theoretic renormalization-group techniques in d=4-epsilon dimensions, we identify a new crossover exponent phi, and compute phi=1+O(epsilon(2)) in the multicritical regime (for small mu(AB)) of the second hierarchy level. In the active phase, we calculate the fluctuation correction to the density exponent on the second hierarchy level, beta(2)=1/2-epsilon/8+O(epsilon(2)). Outside the multicritical region, we discuss the crossover to ordinary DP behavior, with the density exponent beta(1)=1-epsilon/6+O(epsilon(2)). Monte Carlo simulations are then employed to confirm the crossover scenario, and to determine the values for the new scaling exponents in dimensions d< or =3, including the critical initial slip exponent. Our theory is connected to specific classes of growth processes and to certain cellular automata, and the above ideas are also applied to unidirectionally coupled pair annihilation processes. We also discuss some technical as well as conceptual problems of the loop expansion, and suggest some possible interpretations of these difficulties.     

Critical dynamic approach to stationary states in complex systems

A dynamic scaling Ansatz for the approach to stationary states in complex systems is proposed and tested by means of extensive simulations applied to both the Bak-Sneppen (BS) model, which exhibits robust Self-Organised Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway, whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations such that ρ(t=0) →0, one observes an initial increase of the density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively; ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS and GOL models, respectively. It is also shown that the temporal autocorrelation decays with exponents C_a = 0.35(2) (C_a = 0.35(5)) for the BS (GOL) model. By using these dynamically determined critical exponents and suitable scaling relationships, we also obtain the dynamic exponents z = 2.10(5) (z = 2.10(5)) for the BS (GOL) model. Based on this evidence we conclude that the dynamic approach to stationary states of the investigated models can be described by suitable power-law functions of time with well-defined exponents.     

Heating of nonequilibrium electrons by laser radiation in solid transparent dielectrics

A computer simulation of the heating of nonequilibrium electrons by an intense high-frequency electromagnetic field leading to the bulk damage of solid transparent dielectrics under single irradiation has been carried out. The dependences of the avalanche ionization rate on threshold field strength have been derived. Using the Fokker-Planck equation with a flux-doubling boundary condition is shown to lead to noticeable errors even at a ratio of the photon energy to the band gap ∼0.1. The series of dependences of the critical fields on pulse duration have been constructed for various initial lattice temperatures and laser wavelengths, which allow the electron avalanche to be identified as a limiting breakdown mechanism. The ratio of the energy stored in the electron subsystem to the excess (with respect to the equilibrium state) energy of the phonon subsystem by the end of laser pulse action has been calculated both with and without allowance for phonon heating. The influence of phonon heating on the impact avalanche ionization rate is analyzed.