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

Monte Carlo studies of critical behaviour of systems with long-range correlated disoder

Monte Carlo simulations of the short-time dynamic behaviour are reported for three-dimensional Ising model and XY-model with long-range spatially correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are computed with the use of the corrections to scaling. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behaviour of this model in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Приводяться Монте Карло симуляції коротко-часової динамічної поведінки для тривимірної моделі Ізинга та XY-моделі з просторовим далекосяжно скорельованим безладом в критичній області, що відповідає лінійним дефектам. Обчислено статичні та динамічні показники з поправками до скейлінгу. Отримані значення показників добре узгоджуються з результатами теоретико-польового опису критичної поведінки цієї моделі в двопетлевому наближені та з нашими результатами Монте Карло симуляцій тривимірної моделі Ізинга в рівноважному стані

Accelerator ELV-12 and its applications in environment protection technologies

For the environment protection purposes, at BINP we developed, designed and manufactured an accelerator ofa new generation ELV-12 with the following parameters: electron energy ranges from 0.6 to 1.0 MeV, beam current is up to 400 mA, beam power up to 400 kW. At present, the accelerator is already manufactured, assembled and all the systems are under adjustment and test.Для природоохоронних застосувань ІЯФ СВ РАН розробив і виготовив прискорювач нового покоління ЕЛВ-12 з наступними параметрами: енергія електронів 0.6...1.0 МеВ, струм пучка до 400 мА, потужність пучка до 400 кВт. В даний час прискорювач виготовлений, зібраний, ведеться налагодження його систем і тестування.Для природоохранных применений ИЯФ СО РАН разработал и изготовил ускоритель нового поколения ЭЛВ-12 со следующими параметрами: энергия электронов 0.6…1.0 МэВ, ток пучка до 400 мА, мощность пучка до 400 кВт. В настоящее время ускоритель изготовлен, собран, ведется отладка его систем и тестирование

Dynamics near the Surface Reconstruction of W(100)

Using Brownian molecular dynamics simulation, we study the surface dynamics near the reconstruction transition of W(100) via a model Hamiltonian. Results for the softening and broadening of the surface phonon spectrum near the transition are compared with previous calculations and with He atom scattering data. From the critical behavior of the central peak in the dynamical structure factor, we also estimate the exponent of the power law anomaly for adatom diffusion near the transition temperature.Comment: 8 pages, 8 figures, to appear in Phys. Rev.

Does strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation towards the Boltzmann equilibrium distribution. The properties of the Levy-flight FFPE derived here are compared with earlier findings for subdiffusive FFPE. The latter is characterized by a non-exponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached and modifications of the Boltzmann thermodynamics are not required

Equivalent Hermitian operator from supersymmetric quantum mechanics

Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $\eta$ operators. We show that despite the fact that an $\eta$ operator produced by a supersymmetric transformation, corresponding to the exact supersymmetry, is singular, it can be used to find the eigenfunctions of a Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once the eigenfunctions of the Hermitian operator are found the operator may be reconstructed with the help of the spectral decomposition.Comment: 9 pages; revised formula (14), published version with erratu

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Critical behavior of magnetic systems with extended impurities in general dimensions

We investigate the critical properties of d-dimensional magnetic systems with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions; both in the case of fixed dimension d=3 and when the space dimension continuously changes from the lower critical dimension to the upper one. The renormalization group calculations are performed in the minimal subtraction scheme. We analyze the two-loop renormalization group functions for different fixed values of the parameters $d, \epsilon_d$. To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the universality class of this system.Comment: 8 figures. To appear in Phys. Rev.

Dynamic structure factor of the Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $\epsilon$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $\omega$ and momentum $k$. In the region we can investigate, $k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation length and $\tau$ the zero-momentum autocorrelation time, deviations are at most of a few percent.Comment: 21 pages, 3 figure

The Harris-Luck criterion for random lattices

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $\phi^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one figure added for clarification, minor re-wordings and typo cleanu