Dynamics of the critical surface in high-intensity laser-solid interactions: modulation of the XUV harmonic spectra

The generation of harmonics from the interaction of an intense (I>or=10(18) W cm(-2)) laser with a solid surface is investigated. Modulation of the harmonic emission spectrum with a periodicity of 2 to 4 harmonics is observed at higher laser intensities. A similar modulation is predicted by a particle-in-cell simulation. The modulation is shown to be caused by the higher modes of oscillation of the critical surface during the interaction. As a result, the dynamics of the critical surface can be inferred from the shape of the harmonic spectrum.     

Critical currents and the critical state in superconductors with magnetic ions

The critical state model is used to derive equations that relate the additional magnetic moment (ΔM) produced by the flux pinning to the critical current density (J_c) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if ΔM is replaced by ΔM/(1 + χ′(H)) where χ′(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J_c values calculated using hysteretic magnetisation measurements without including the term χ′(H), can be in error by factors of 7.     

Universality of the ratio of the critical amplitudes of the magnetic susceptibility in a two-dimensional ising model with nonmagnetic impurities

The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q _c = 0.407254). The behavior of the effective critical exponent γ(q) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.     

Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method,we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice.We determine critical lines belong to the three-dimensional XY universality class in variable of θ(2θ) between the XY-ferromagnetic(nematic) and disordered states.Furthermore,the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class.The critical points are determined from the intersections of Binder ratios for various system sizes.With two sets of critical points obtained,we finally construct the phase diagram on the-J plane.     

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.     

Geometrical approach to the thermodynamical theory of phase transitions of the second kind

A geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure P and variable temperature T is proposed. Equilibrium states of a system at zero external field and fixed P and T are described by points in three-dimensional space with coordinates η, the order parameter, T, the temperature and /gf, the thermodynamic potential. These points form the so-called zero field curve in the (η, T, /gf) space. Its branch point coincides with the critical point of the system. The small parameter of the theory (the distance from the critical point along the zero-field curve) is shown to be more convenient than the small parameter of the Landau theory. It is emphasized that no explicit functional dependency of /gf on η and T is imposed.

It is shown that using (η, T, /gf) space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on η and T, but also on near (local) order parameters λ_i. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature T_c.     

Compensation for the thermal effect in the second-harmonic generation of a Q-switched nanosecond-kilohertz Nd:YVO4 laser

We report the quantitative relationship between the phase-matching condition and the surrounding temperature in a critical phase-matching second-harmonic generation of a Q-switched Nd:YVO₄ laser with a high repetition rate. The thermal effect can be effectively compensated for by appropriately changing the phase-matching angle with respect to the surrounding temperature of a nonlinear optical crystal. A stable wavelength conversion from the 1064 nm fundamental to the 532 nm second harmonic in a type-I critical phase-matching lithium triborate crystal is experimentally achieved and the corresponding conversion efficiency up to 70% is obtained.     

Allowance for the solar-magnetospheric connections in a problem of predicting the critical frequency of the subauroral ionosphere

The cause-and-effect relation between variations in the critical frequency of the F ₂ subauroral ionospheric layer and the key solar-magnetospheric parameters is studied. The features of the dependence of the critical frequency of the subauroral ionosphere on the value and components of the interplanetary magnetic field, the solar-wind parameters, the X-ray and ultraviolet radiation intensities, the solar zenith angle, and the intensity of precipitation of low-energy particles are established. Within the framework of this study, codes allowing one to solve the problems of predicting the critical frequency of the ionosphere by the method of artificial neural networks has been developed. The neural-network forecasting experiments reveal the characteristic times of the ionospheric response to magnetospheric disturbancs. The found optimal architecture of the neural network allows us to predict the time series of the critical frequency of the high-latitude ionosphere for the interval 0.5–3 h with an accuracy of up to 93%. The obtained linear and nonlinear dependences of the critical frequency of the ionospheric F ₂ layer on the geophysical parameters can be used for developing ionospheric models required for determining the maximum usable frequency of HF radio communication. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 2, pp. 109–117, February 2009.     

Renormalized loop expansion to compute finite size effects of the constraint effective potential

In latticeφ ⁴ close to the critical line, finite size effects can be computed by renormalized loop expansions. In order to do so, the constraint effective potential is computed to two loop order. Using this expression, we are able to extract results for renormalized masses and coupling constants from Multigrid Monte Carlo data of Mack and Meyer for the constraint effective potential close to the critical line, and compare them with the analytical results ofLüscher and Weisz. Perfect agreement is found.     

Heat capacity of a Cr2O3 antiferromagnet near the critical temperature

The heat capacity of a Cr₂O₃ antiferromagnet near the critical temperature is precisely measured by ac calorimetry. The critical behavior of the heat capacity is examined. The regularities of variations in the universal critical parameters near the critical point are determined, and their values are calculated. A crossover from the Heisenberg (n=3) to the Ising (n=1) critical behavior is revealed.     

Influence of Ag doping on the critical behavior of the heat capacity of manganites

The critical behavior of the heat capacity of Ag doped manganites is studied. Changing regularities of universal critical parameters near the critical point are determined. All investigated samples up to t _min ≈ 10^?3 correspond to 3D Heisenberg universality class of the critical behavior. The universality class of critical behavior of La_{1 – x} Ag _y MnO₃ (y ≤ x) heat capacity is shown to be Ag-concentration independent.     

Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map

The spectrum and eigenfunctions of the Frobenius-Perron operator induced by the tent map are discussed in detail. Special attention is paid to the case where the critical point of the map lies on an aperiodic trajectory and the differences from maps with a periodic critical trajectory are stressed. It is shown that the relevant eigenvalues of the spectrum are not sensitive to the aperiodicity of the critical trajectory. All other parts of the spectrum and all eigenfunctions in particular are changed drastically if the critical trajectory becomes aperiodic. The intimate connection between the point spectrum and the kneading invariant is established and the critical slowing down as well as the band splitting are a consequence of its properties. The structure of the infinite sequence of null spaces and its implications on the spectrum of the operator are discussed. It is shown that any initial distributionP(0,x) of bounded variation can be projected uniquely onto the eigenfunctions of the relevant eigenvalues and that the time dependence ofP(n, x) is determined by this expansion up to an errorO( ⁿ). From this the stationary and the asymptotic behavior of the correlation function x(n) x can be derived exactly.     

Thermodynamic properties of multicomponent mixtures near the liquid-vapor critical point

A new method has been proposed to describe the physical properties of multicomponent mixtures near their critical points. The method is based on the transition from the experimental thermodynamic variables to scaling fields, is applicable to a mixture with any number of the components, and is, thus, universal. For the previously studied methane-propane-pentane mixture, it has been shown that the anomalies of the specific heat at a constant volume and derivative (?P/?T)_ρ,x can be quantitatively described in this approach in a wide vicinity of a critical point, including noncritical isochores.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Melting and wetting transitions in the three-state chiral clock model

The melting transition of the two-dimensional, three-state, asymmetric or chiral clock model is examined. Evidence from scaling arguments and analysis of perturbation series is presented, indicating that the chiral symmetry-breaking operator is relevant at the symmetric (or pure Potts) critical point with a crossover exponent of ø ≈ 0.2. The remainder of the commensurate-disordered phase boundary therefore appears to be in a new universality class, distinct from the pure three-state Potts transition. An interfacial wetting transition that plays an important role in the crossover between the two types of critical behavior is discussed. The location and exponents of this wetting transition are obtained both in a low-temperature limit using generating function techniques and in a systematic low-temperature expansion of the transfer matrix.     

Theoretical study of the critical current of YBa2Cu3O7−δ bicrystals with hole-deficient grain boundaries

We develop a theory of the critical current across grain boundaries in YBa₂Cu₃O_7−δ bicrystals. Experiments have shown that there is hole depletion near a boundary and the concentration profiles have been determined for specific cases. These results mean that the critical temperature is a function of distance from the boundary. Taking this function from experiment as input into the theory, we study two specific boundaries: a boundary with a 7° misorientation angle about [100] which is known to be strongly coupled for the purposes of current flow, and a 31° boundary which is known to be weakly coupled. Using Ginzburg-Landau theory, we determine the dependence of the critical current density (j_c) on temperature and the spatial dependence of the order parameter for these boundaries. The results show that the oxygen depletion can account for a major portion of the change from weak to strong coupling of boundaries as the misorientation angle is increased.     

Critical behaviour of the hard-core lattice gas on the honeycomb lattice

The hard triangle lattice-gas model (lattice-gas on the honeycomb lattice with first neighbour exclusion) is studied by the phenomenological renormalization method. The critical activity is found to be z = 7.85 and the critical exponents suggest that this model belongs to the 2-D Ising universality class.     

Spontaneous-search method and short-time dynamics: applications to the Domany-Kinzel cellular automaton

The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν_⊥. Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation.     

On the contribution of nearly critical spin and charge collective modes to the Raman spectra of high-Tc cuprates

We discuss how Raman spectra are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover, spin modes should be more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuate with high frequency.