Metastability of defects,potential fluctuations,and percolation transition in GaAs

Potential fluctuations due to donor–acceptor compensation have been used to observe localization–delocalization transition in semi-insulating GaAs. Photoinduced transients, resulting from relaxation of stored charges in potential valleys, have two components. The long-lived power law decay at low temperature signifies a microscopically inhomogeneous disordered phase, and single exponential decay at a higher temperature signifies a homogeneous ordered phase. Temperature dependence of steady state photocurrent and kinetics of photocurrent decay suggest percolation as a possible mechanism for photoinduced transition in semi-insulating GaAs.     

Continuous Replica Symmetry Breaking in Critical Phenomena in Disordered Ferromagnets

The replica symmetry breaking (RSB) in critical phenomena in disordered ferromagnets is studied. We modified the assumption of Dotsenko et al. about the local minimum solutions of the Hamiltonian with random temperature. It is shown explicitly that the continuous RSB is generated in the renormalization group (RG). The physical regime of the coupling constants are investigated through the RG equations.     

Stability of the critical behavior of weakly disordered systems against replica symmetry breaking

A field-theoretical approach is used to describe the critical behavior of weakly disordered systems with a p-component order parameter. Renormalization group (RG) analysis of the effective replica Hamiltonian of a model with replica-unsymmetrical interaction potential is carried out in a two-loop approximation directly for three-dimensional systems. The Padé-Borel summation technique is used to determine fixed points of the RG equations for the case of a single-step replica symmetry breaking (RSB). Analysis of their stability showed that the type of stable critical behavior of the disordered systems against the RSB effects remains as before.     

Field theory of Ising percolating clusters

The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable field theory and identify the non-perturbative mechanism which allows the percolative transition in absence of thermodynamic singularities. The analysis is extended to the Kertész line along which the Coniglio–Klein droplets percolate in a positive magnetic field.     

Phase transition and critical dynamics in site-diluted Josephson-junction arrays

Measurements of the IV characteristics of site-diluted Josephson-junction arrays have revealed intriguing effects of percolative disorder on the phase transition and the vortex dynamics in a two-dimensional XY system. Different from other types of phase transitions, the Kosterlitz-Thouless transition was eliminated with the introduction of percolative disorder far below the percolation threshold. Even after the Kosterlitz-Thouless order had been removed, the system remained superconducting at low temperatures by establishing a different type of order. Near the percolation threshold, evidence was found that, as a consequence of the underlying fractal structure, the critical dynamics of the phase degrees of freedom persisted down to zero temperature.     

Dynamical conductivity at the dirty superconductor-metal quantum phase transition

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments.     

Crossover scale of the fixed point with replica symmetry breaking in the random Potts model

We study the scaling properties of the renormalization group (RG) flows in the two-dimensional random Potts model, assuming a general type of replica symmetry breaking (RSB) in the renormalized coupling matrix. It is shown that in the asymptotic regime the RG flows approach the non-trivial RSB fixed point algebraically slowly, which reflects the fact that this type of the fixed point is marginally stable. As a consequence, the crossover spatial scale corresponding to the critical regime described by this fixed point turns out to be exponentially large. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 11, 718–723 (10 December 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Inhomogeneous ordered states and translational nature of the gauge group in the landau continuum theory: I. General analysis

A phenomenological continuum theory of phase transitions to a global inhomogeneous state of a crystal must take into account the compensating fields that represent the fields of stresses caused by dislocations appearing at the boundaries between local homogeneous regions. These compensating fields, which are introduced in order to satisfy the condition of invariance of the Landau potential with respect to the operation of translation, enter into the theory via extended derivatives of the local order parameters with respect to macroscopic coordinates of the local homogeneous regions in the crystal. Because of this extension of derivatives, the theory of phase transitions to an inhomogeneous state must include the theory of elasticity, in which a potential of the stress field induced by the phase transition is proportional to the compensating field magnitude. The Kröner equation, which describes the state of dislocations induced by spatially inhomogeneous ordering, appears in this theory as a result of minimization of the Landau potential with respect to the compensating fields.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Lynden-Bell and Tsallis distributions for the HMF model

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial condition takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Such distributions have recently been observed in direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve corresponding to the Lynden-Bell statistics in relation with the HMF model and analyze the dynamical and thermodynamical stability of spatially homogeneous solutions by using two general criteria previously introduced in the literature. We express the critical energy and the critical temperature as a function of a degeneracy parameter fixed by the initial condition. Below these critical values, the homogeneous Lynden-Bell distribution is not a maximum entropy state but an unstable saddle point. Known stability criteria corresponding to the Maxwellian distribution and the water-bag distribution are recovered as particular limits of our study. In addition, we find a critical point below which the homogeneous Lynden-Bell distribution is always stable. We apply these results to the situation considered in Antoniazzi et al. For a given energy, we find a critical initial magnetization above which the homogeneous Lynden-Bell distribution ceases to be a maximum entropy state. For an energy U=0.69, this transition occurs above an initial magnetization M_x=0.897. In that case, the system should reach an inhomogeneous Lynden-Bell distribution (most mixed) or an incompletely mixed state (possibly fitted by a Tsallis distribution). Thus, our theoretical study proves that the dynamics is different for small and large initial magnetizations, in agreement with numerical results of Pluchino et al. (2004). This new dynamical phase transition may reconcile the two communities by showing that they study different regimes.     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Percolation in Media with Columnar Disorder

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.     

Coulomb-frustrated phase separation phase diagram in systems with short-range negative compressibility

Using numerical techniques and asymptotic expansions we obtain the phase diagram of a paradigmatic model of Coulomb-frustrated phase separation in systems with negative short-range compressibility. The transition from the homogeneous phase to the inhomogeneous phase is generically first order in isotropic three-dimensional systems except for a critical point. Close to the critical point, inhomogeneities are predicted to form a bcc lattice with subsequent transitions to a triangular lattice of rods and a layered structure. Inclusion of a strong anisotropy allows for second- and first-order transition lines joined by a tricritical point.     

On Inhomogeneous Polarized States near the Phase Transition Point in a Thin Ferroelectric Film

It is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector k_⊥ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.     

Lamellar-like structures in ferrofluids placed in strong magnetic fields

We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipole–dipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.     

Electrical properties of orbitally oriented crystals allowing for electron-deformation interaction

This paper studies the effect of orbital ordering of the electron density on the electrical properties of transition metal compounds including electron-deformation [strain] interaction. The electrical conductivity was calculated on the basis of the Kubo equation. It is shown that in a certain temperature region, orbital ordering is realized in the electron subsystem. The destruction of the ordered state can take place by a I or II order phase transition as a function of the amount of electron-deformation interaction. There is a finite jump in the electrical conductivity function at the point of disorder. The activation energy in the ordered state is greater than in the disordered state. The results of the calculations coincide with the experimental data on the electrical resistance of compounds with a spinel and perovskite structure containing Jahn-Teller ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 31–36, December, 1986.The authors express their gratitude to I. Ya. Kanovskii for his valuable discussions on the obtained results.     

Evolution of a Magnetoresonance Line Near to a Limit of Percolation in Dilute Magnetics

In paper the results of numerical modeling of a magnetic resonance in dilute magnetics near to a threshold of a percolation are discussed. The classical equation of motion of magnetic moments is used in view of an exchange interaction such as RKKI and imitation of spin-phonon interaction by Monte-Carlo method. It is shown, that cluster structure of a magnetic and threshold of percolation are determined by critical distance, on which there is a change of a sign of an exchange interaction. In an examination of percolation phase transition the jump change of breadth of a line of a magnetic resonance is set, that can form the basis for experimental definition of a threshold percolation and parameters of an exchange interaction by methods of a radiospectroscopy.     

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: a replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.