Stability of critical behaviour of weakly disordered systems with respect to the replica symmetry breaking

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For case with 1-step RSB the fixed points (FP's) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FP's has shown a stability of the critical behaviour of the weakly disordered systems with respect to RSB effects and realization of former scenario of disorder influence on critical behaviour.Comment: 10 pages, RevTeX. Version 3 adds the $\beta$ functions for arbitrary dimension of syste

Critical behavior of disordered systems with replica symmetry breaking

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $\epsilon$-expansion and the scope of the method applicability is determined.Comment: 18 pages, 2 figure

Critical Behaviour of 3D Systems with Long-Range Correlated Quenched Defects

A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations $\sim |{\bf x}|^{-a}$ for large separations ${\bf x}$ is given. Directly for three-dimensional systems and different values of correlation parameter $2\leq a \leq 3$ a renormalization analysis of scaling function in the two-loop approximation is carried out, and the fixed points corresponding to stability of the various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by double $\epsilon, \delta$ - expansion. The critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.Comment: Submitted to J. Phys. A, Letter to Editor 9 pages, 4 figure

New spherically symmetric monopole and regular solutions in Einstein-Born-Infeld theories

In this work a new asymptotically flat solution of the coupled Einstein-Born-Infeld equations for a static spherically symmetric space-time is obtained. When the intrinsic mass is zero the resulting spacetime is regular everywhere, in the sense given by B. Hoffmann and L. Infeld in 1937, and the Einstein-Born-Infeld theory leads to the identification of the gravitational with the electromagnetic mass. This means that the metric, the electromagnetic field and their derivatives have not discontinuities in all the manifold. In particular, there are not conical singularities at the origin, in contrast to well known monopole solution studied by B. Hoffmann in 1935. The lack of uniqueness of the action function in Non-Linear-Electrodynamics is discussed.Comment: Final version in journal. Amplied version with new results that previous talk in Protvino worksho

Vacuum polarization in a cosmic string spacetime induced by flat boundary

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string.Comment: 12 pages, 5 figures, talk presented at the 8th Alexander Friedmann International Seminar on Gravitation and Cosmology, in Rio de Janeiro, Brazi

Relaxational dynamics in 3D randomly diluted Ising models

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).Comment: 38 page

Theory of the microwave induced zero resistance states in two-dimensional electron systems

The phenomena of the microwave induced zero resistance states (MIZRS) and the microwave induced resistance oscillations (MIRO) were discovered in the ultraclean two-dimensional electron systems in 2001 -- 2003 and have attracted great interest of researchers. In spite of numerous theoretical efforts the true origin of these effects remains unknown so far. We show that the MIRO/ZRS phenomena are naturally explained by the influence of the ponderomotive forces which arise in the near-contact regions of the two-dimensional electron gas under the action of microwaves. The proposed analytical theory is in agreement with all experimental facts accumulated so far and provides a simple and self-evident explanation of the microwave frequency, polarization, magnetic field, mobility, power and temperature dependencies of the observed effects.Comment: 18 pages, 9 figures, resubmission. Essential modifications/additions: Section I, Section II.5 and Fig. 5, Section IV, Reference

Survival of interacting Brownian particles in crowded 1D environment

We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle interaction. Due to the absorbing boundary the number of particles in the pore gradually decreases. We present the exact analytical solution of the problem. Our procedure merely requires the knowledge of the corresponding single-particle problem. First, we calculate the simultaneous probability density of having still a definite number $N-k$ of surviving particles at definite coordinates. Focusing on an arbitrary tagged particle, we derive the exact probability density of its coordinate. Secondly, we present a complete probabilistic description of the emerging escape process. The survival probabilities for the individual particles are calculated, the first and the second moments of the exit times are discussed. Generally speaking, although the original inter-particle interaction possesses a point-like character, it induces entropic repulsive forces which, e.g., push the leftmost (rightmost) particle towards (opposite) the absorbing boundary thereby accelerating (decelerating) its escape. More importantly, as compared to the reference problem for the non-interacting particles, the interaction changes the dynamical exponents which characterize the long-time asymptotic dynamics. Interesting new insights emerge after we interpret our model in terms of a) diffusion of a single particle in a $N$-dimensional space, and b) order statistics defined on a system of $N$ independent, identically distributed random variables

Calculations of the dynamical critical exponent using the asymptotic series summation method

We consider how the Pad'e-Borel, Pad'e-Borel-Leroy, and conformal mapping summation methods for asymptotic series can be used to calculate the dynamical critical exponent for homogeneous and disordered Ising-like systems.Comment: 21 RevTeX pages, 2 figure