Multifractality in elastic percolation

We present numerical results on the distribution of forces in the central-force percolation model at threshold in two dimensions. We conjecture a relation between the multifractal spectrum of scalar and vector percolation that we test for central-foce percolation. This relation is in excellent agreement with our numerical data.     

On the upper critical dimension of Bernoulli percolation

We derive a set of inequalities for thed-dimensional independent percolation problem. Assuming the existence of critical exponents, these inequalities imply: $$\begin{gathered} f + v \geqq 1 + \beta _Q , \hfill \\ \mu + v \geqq 1 + \beta _Q , \hfill \\ \zeta \geqq \min \left\{ {1,\frac{{v^, }}{v}} \right\}, \hfill \\ \end{gathered} $$ where the above exponents aref: the flow constant exponent, ν(ν′): the correlation length exponent below (above) threshold, μ: the surface tension exponent, β _Q : the backbone density exponent and ζ: the chemical distance exponent. Note that all of these inequalities are mean-field bounds, and that they relate the exponentv defined from below the percolation threshold to exponents defined from above threshold. Furthermore, we combine the strategy of the proofs of these inequalities with notions of finite-size scaling to derive: $$\max \{ dv,dv^, \} \geqq 1 + \beta _Q ,$$ whered is the lattice dimension. Since β _Q ≧2β, where β is the percolation density exponent, the final bound implies that, below six dimensions, the standard order parameter and correlation length exponents cannot simultaneously assume their mean-field values; hence an implicit bound on the upper critical dimension:d _c ≧6.     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

Are spin-dependent forces in charmonium generated through scalar-vector admixture?

I show that if the spin-dependent confining forces are generated through scalar-vector admixture then the ³p_J splittings restrict the vector to scalar ratio to be less than half. Further it is shown that an accurate measurement of the ¹p₁ mass can clearly distinguish this model from vector and scalar exchange models.     

Theoretical justification of the magnetic phase diagram of CuMn alloys

Some important observations on the magnetic susceptibility of concentration Cumn alloys by Gibbs et al. are reinterpreted in the light of the mean-field theory of classical vector spin models with competing exchange interactions. The phase diagram proposed by Gibbs et al. is shown to be in qualitative agreement with the corresponding phase diagram predicted by mean-field theory.     

Influence of frustration on a d = 3 diluted antiferromagnet: FexZn1−xF2

The influence of a frustrated bond on the magnetic properties of a d = 3 uniaxial (Ising) bcc diluted antiferromagnet, with emphasis in the compounds FexZn_1−xF₂, is investigated by a local mean-field numerical simulation. In particular we find that the initial drop of the saturation staggered magnetization (M_S) with concentration follows a percolation-like phenomenon characterized by an exponent β_P. For the frustrated samples, however, this regime is followed by a second one identified by a ‘long tail’ effect such that M_S is zero only at the percolation threshold. Our numerical data also confirms a spin-glass phase near this threshold.     

Vibrational properties of bond-diluted triangular lattices

Vibrational properties of two-dimensional (2D) triangular elastic bond percolation systems with scalar, central, and bond-bending forces are studied by using the HCPA, the recursion method and the replica trick. The densities of states calculated by means of the HCPA agree qualtatively well with corresponding results of the recursion method. The low-frequency behaviour of the density of states can be interpreted in terms of a phonon-fracton crossover. The dynamic structure factor calculated with the aid of the HCPA for the scalar model exhibits for any wave vector only a single peak, contrary to threedimensional systems.     

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.     

Estimation of Critical Point in Branching Reactions: Further Examination of Gel Point Formula

The theory of gel point in real polymer solutions is examined with the empirical correlation between the reciprocal of the percolation threshold and the coordination number given by the percolation theory. Applying a larger value of the relative frequency of cyclization, an excellent agreement is obtained between the present theory and the percolation result. This suggest that while the ring distribution on lattices is similar to that in real systems, ring production is more frequent in the lattice model than in real systems. To confirm this conjecture, we derive the ring distribution function of the lattice model as a limiting case of d→∞, and show that the solution is in fact identical to the asymptotic formula of C→∞ in real systems except for the coefficient C, which has a maximum at d = 5, in support of the above conjecture. To examine the validity of the asymptotic solution for the lattice model, we apply it to the critical point problem of the percolation theory, showing that the solution works well in high dimensions greater than six.     

The scalar contribution toτ →K πν τ

We consider the scalar form factor inτ →K πν _τ decays. It receives contributions both from the scalar resonanceK*₀(1430) and from the scalar projection of off-shell vector resonances. We construct a model for the hadronic current which includes the vector resonancesK*(892) andK*(1410) and the scalar resonanceK*₀(1430). The parameters of the model are fixed by matching to theO(p ⁴) predictions of chiral perturbation theory. Suitable angular correlations of theKπ system allow for a model independent separation of the vector and scalar form factor. Numerical results for the relevant structure functions are presented.     

The supergroup manifold formulation of the Wess-Zumino multiplet revisited: The supercurrent and the supergravity auxiliary fields

In this paper we provide a consistent first-order group-manifold formulation of the Wess-Zumino system. It is shownhow the well-known auxiliary fields of the ($\text{1}\text{2}$, 0, 0) system arise by supplementing Bianchi identities with the “second-order constraints”; that is, those equations allowing the transition from the first order to the second order of the theory. When the ($\text{1}\text{2}$, 0, 0) multiplet is coupled to N = 1 supergravity and the torsion “second-order constraint” is implemented, we get a non-minimal set of auxiliary fields (scalar, pseudoscalar axial vector and a spinor). We argue this to be the fundamental set of auxiliary fields. The so-called “minimal set” is not coordinate invariant and can be recovered only by adding a non-geometrical constraint.     

Mean-Field Behavior for the Survival Probability and the Percolation Point-to-Surface Connectivity

We consider the critical survival probability (up to timet) for oriented percolation and the contact process, and the point-to-surface (of the ball of radiust) connectivity for critical percolation. Let θ_t denote both quantities. We prove in a unified fashion that, if θ_t exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then θ_t=t^-1 for the time-oriented models with d > 4 and θ_t=t^-2 for percolation with d > 7.     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

Mean field model for relativistic heavy ion collisions

We take up a relativistic mean-field model consisting out of nucleons coupled to a scalar and a vector meson. We solve the corresponding time-dependent mean-field equations on a three-dimensional grid. Results for¹⁶O +¹⁶O scattering at various energies and various impact parameters show significant differences with conventional TDHF calculations. We see sidewards collective flow similar as in fluid dynamics and in experiment. We observe complete spallation and remarked oscillations of the meson fields.     

Percolation of polyatomic species on a simple cubic lattice

In the present paper, the site-percolation problem corresponding to linear k-mers (containing k identical units, each one occupying a lattice site) on a simple cubic lattice has been studied. The k-mers were irreversibly and isotropically deposited into the lattice. Then, the percolation threshold and critical exponents were obtained by numerical simulations and finite-size scaling theory. The results, obtained for k ranging from 1 to 100, revealed that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the k-mer size; and (ii) the phase transition occurring in the system belongs to the standard 3D percolation universality class regardless of the value of k considered.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.