Phase Transition in a Generalized Eden Growth Model on a Tree

We study analytically the late time statistics of the number of particles in an Eden growth model on a tree. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c ^−l where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a ‘phase transition’ at a critical value . While for the variance is proportional to the mean and the distribution is normal, for the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with m branches and, in this more general case, we show that the critical point occurs at .     

Phase Structure of Systems with Infinite Numbers of Absorbing States

Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to describe the critical behavior of such systems, and also introduce and study a non-Markovian discrete model, which is argued to present the same critical features. On the basis of mean-field analysis, Monte Carlo simulations, and theoretical arguments, we conclude that the phenomenology of the non-Markovian models closely parallels that of systems with many absorbing states in one and two dimensions. The bulk or static critical properties of these systems fall in the directed percolation (DP) universality class. By contrast, the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior: Depending on parameter values they can, both in one and two dimensions, fall either in the dynamical percolation or DP universality class, or else exhibit apparently nonuniversal exponents. In contrast to previous results, however, the nonuniversal exponents in 2D are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes DP values. These results demonstrate the efficacy of the non-Markovian approach for understanding systems with many absorbing states, which are difficult to analyze in their original microscopic formulation.     

Nonlinear excitations and electric transport in dissipative Morse-Toda lattices

We investigate the onset and maintenance of nonlinear soliton-like excitations in chains of atoms with Morse interactions at rather high densities, where the exponential repulsion dominates. First we discuss the atomic interactions and approximate the Morse potential by an effective Toda potential with adapted density-dependent parameters. Then we study several mechanisms to generate and stabilize the soliton-like excitations: (i) External forcing: we shake the masses periodically, mimicking a piezoelectric-like excitation, and delay subsequent damping by thermal excitation; (ii) heating, quenching and active friction: we heat up the system to a relatively high temperature Gaussian distribution, then quench to a low temperature, and subsequently stabilize by active friction. Finally, we assume that the atoms in the chain are ionized with free electrons able to move along the lattice. We show that the nonlinear soliton-like excitations running on the chain interact with the electrons. They influence their motion in the presence of an external field creating dynamic bound states (“solectrons”, etc.). We show that these bound states can move very fast and create extra current. The soliton-induced contribution to the current is constant, field-independent for a significant range of values when approaching the zero-field value.     

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.Research supported by U.S. National Science Foundation under grants GP-40768X (F.J.D.), MCS 75-21684 (E.H.L.), and GP-39048 (B.S.).Alfred Sloan Fellow.     

Phase transitions in polymesomorphic compounds

Summary The results of a X-ray diffraction study, performed on N(p-n-pentyloxy benzylidene)p′-n-octylaniline (50.8) and N(p-n-pentyloxy benzylidene)p′-n-decylaniline (50.10) are presented. The investigated compounds exhibit smecticB, smecticA and nematic phases in between solid and isotropic liquid phases. In addition, after a thermal cycle the 50.8 compound exhibits a smecticG phase at room temperature. The interlayer and the in-plane intermolecular distances were obtained as functions of temperature through all the mesophases. A phase coexistence has been observed during the solid to smecticB and the smecticB to smecticA phase transitions of the 50.8 compound. The nematic to smecticA phase transitions are found to be of second order for both compounds. Pretransitional effects due to cybotactic-cluster formation in the nematic region are observed.

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Riassunto Si presentano i risultati di uno studio effettuato mediante la diffrazione dei raggi X sul N(p-n-pentilossi benzilidene)p′-n-ottilanilina (50.8) e sul N(p-n-pentilossi benzilidene)p′-n-decilanilina (50.10). Tra le fasi solida ed isotropica i composti esaminati presentano le mesofasiS _B ,S _A e nematica. Inoltre, dopo un ciclo termico il composto 50.8 presenta una faseS _G a temperatura ambiente. Sono state misurate le distanze tra i piani smettici e le distanze laterali tra le molecole in tutte le mesofasi in funzione della temperatura. Una coesistenza di fase è stata osservata durante le transizioni solido →S _B eS _B →S _A del composto 50.8. Le transizioni nematico-S _A sono risultate del second'ordine per entrambi i composti. Nelle fasi nematiche sono stati osservati effetti pretransizionali dovuti alla formazione di gruppi cibotattici.

     

Criteria for local equilibrium in a system with transport of heat and mass

Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to T=0.09 and weight-fraction gradients up to w ₁=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be T0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.     

Phase transitions and metastable states in TlGaSe2

The results of measurements of the dielectric constant of TlGaSe₂ in temperature range of successive phase transitions are presented. An anomaly in the temperature dependence of the real part of dielectric constant in TlGaSe₂ has been observed at about 242?K in addition to anomalies at 115, 108, and also near 65?K as reported in previous publications. The presence of temperature hysteresis effects in temperature interval between 115 and 242?K allowed making a conclusion about possible existence of an incommensurate phase in the mentioned temperature range. A model of succession of the structural phase transitions in TlGaSe₂ has been suggested.     

Phase transitions of a feedback amplifier

The phase transition behaviour of an amplifier with positive feedback is experimentally studied. The results are interpreted using catastrophe theory language. Zero (in Gilmore’s classification), first and second-order transitions are demonstrated by driving the system along appropriate trajectories in control parameter space and the cusp and the spinodal are mapped. The fluctuations of the order parameter are investigated and their relationship to system response time established. Quench experiments analogous to those familiar in condensed matter have also been performed and with similar results.     

Phase diagram of the frustrated spin ladder with the next nearest intrachain couplings

By the density matrix renormalization group method, the phase diagram of the frustrated spin-1/2 ladder with the next nearest intrachain and ferromagnetic interchain couplings is obtained. According to our results, the two-rung entanglement is shown to be more sensitive than order parameters for determining phase boundary in such a frustrated spin ladder model. Furthermore, the additional next nearest intrachain coupling is found to enhance the intermediate columnar dimerized phase evidently.     

Propagation and ignition of fast gasless detonation waves of phase or chemical transformation in condensed matter

Fast self sustained waves of chemical or phase transformations, observed in several contexts in condensed matter effectively result in “gasless detonation". The phenomenon is modelled by coupling the reaction diffusion equation, describing chemical or phase transformations, and the wave equation, describing elastic perturbations. The coupling considered in this work involves (i) a dependence of the sound velocity on the chemical (phase) field, and (ii) the destruction of the initial chemical equilibrium when the strain exceeds a critical value (strain induced phase transition). Both the case of an initially unstable state (first order kinetics) and metastable state (second order kinetics) are considered. An exhaustive analytic and numerical study of travelling waves reveals the existence of supersonic modes of transformations. The practically important problem of ignition of fast waves by mechanical perturbation is investigated. With the present model, the critical strain necessary to ignite gasless detonation by local perturbations is determined. Received 18 November 1999     

Chiral Magnetic Effect and Chiral Phase Transition

We study the influence of the chiral phase transition on the chiral magnetic effect. The azimuthal charge-particle correlations as functions of the temperature are calculated. It is found that there is a pronounced cusp in the correlations as the temperature reaches its critical value for the QCD phase transition. It is predicted that there will be a drastic suppression of the charge-particle correlations as the collision energy in RHIC decreases to below a critical value. We show then the azimuthal charge-particle correlations can be the signal to identify the occurrence of the QCD phase transitions in RHIC energy scan experiments.     

Phase transition studies in polymesomorphic compounds

Summary The structural parameters of theS _A andS _B mesophases and the phase transitionS _G -S _B andS _B -S _A of the compound N-(p-n-octyloxybenzylidene)p-n-butyl aniline were investigated by X-ray diffraction. This work is complementary to the previous structural determination in the crystalline solid phase andS _G phase of the same compound. TheS _B hexagonal lattice parameters atT=66°C area=b=(5.03±0.01) ? andc=(27.6±0.2) ?. TheS _A structural data atT=80°C are layer thicknessd=(26.9±0.2) ? and intermolecular distanceD=(5.04±0.05) ?. The interlayer and the in-plane intermolecular distances were obtained as a function of temperature through all the mesophases. Pretransitional effects were observed at theS _G -S _B phase transition, which corresponds to a progressive reduction to zero of the molecule inclination angle with respect to the normal to the smectic layers. The layer thickness in theS _A phase appeared smaller than that in theS _B due to molecular axial fluctuations. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Phase transitions and electrical characteristics of tungsten substituted barium titanate

In the present work, phase transitions and electrical characteristics of tungsten substituted barium titanate are reported. Structural analysis of the prepared samples was carried out to confirm the formation of the compounds in proper phase. Scanning electron micrographs of the compounds have been used to investigate the grain morphology of the material. The dielectric properties of the samples have been studied as a function of temperature and frequency. The variation of dielectric constant (ε_r) with temperature shows a diffuse kind of ferro–paraelectric phase transition. The diffusitivity of the phase transitions has been calculated. Complex impedance spectroscopy analysis was carried out to investigate the electrical characteristics of the specimen.     

Topological Phase Transition and Phase Diagrams in a Two-Leg Kitaev Ladder System

A scheme to investigate the topological properties in a two-leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non-identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.     

Phase boundary of dilute lattice spin glasses

Based on a recently developed algorithm for the exploration of ground states in bond-diluted lattice spin glasses, we determine the scaling of defect energies with system size for Ising spin glasses at the bond percolation threshold p_c. The results can be related by well-known scaling relations to the shape of the transition temperature T_g∼(p-p_c)^φ between the paramagnetic and glassy regime for p→p_c. The numerical results in three dimensions are consistent with rather old experimental data for (Fe_xNi_1-x)₇₅P₁₆B₆A₃, suggesting that new experimental work may be able to put those numerical predictions to the test.     

Collective behavior of coupled nonuniform stochastic oscillators

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α^′<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.     

Study of Phase Transition Properties in Epitaxial Ferroelectric Film

Based on the transverse Ising model and using decoupling approximation to the Fermi-type Green＇s function, we study the phase transition properties of the epitaxial ferroeleetric film with one substrate. A general recursive equation of the ferroelectric thin film with two n-layer materials is obtained, which enables us to study the phase transition properties for any number layers for epitaxial ferroelectric thin film. With the help of this equation, we analyze the effect of the exchange interaction and the transverse field in the phase diagram, the influence to the polarizations and Curie temperature numerically. The results show that epitaxial ferroelectric film are able to induce a strong increase or decrease of Curie temperature to different exchange interactions and transverse fields within the epitaxial film layers. The theoretical results are in reasonable accordance with experimental data of different ferroelectric thin film.     

Topological Phase Transition of Non-Hermitian Crosslinked Chain

The contents of topological classification of matter are enriched by non-Hermiticity, such as exceptional points, bulk-edge correspondence, and skin effects. Physically, gain and loss can be introduced by imaginary on-site potentials of lattice Hamiltonians, and the topological phase transition for a cross-linked chain in the presence of such non-Hermiticity is investigated. The topological phase diagram in terms of a winding number is obtained analytically with phase boundaries coinciding with the surfaces of exceptional points. The topologically original edge states with distribution mainly at the joints between domains of different phases are protected even for long chains. The non-Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies, expected values of Pauli matrices, and trajectories of these quantities. This model may be implemented in coupled photonic crystals, fermions trapped in optical lattice, or non-Hermitian electrical-circuit lattices, and the edge states are immune to various kinds of disorders until topological phase transition occurs. This work gives insight into the influence of non-Hermiticity on topological phase of matter.     

Phase diagrams and dielectric studies of binary mixtures exhibiting intermediate nematic and induced smectic phases

Investigations on the phase diagrams of two bi-component mixtures of liquid crystals are presented. Whereas in one of the bi-component systems, smectic A (SmA) phase is seen to be induced, in the other case the so-called nematic “island” has been observed. The dielectric properties of magnetically oriented sample forming nematic phase and induced smectic phase in one of the mixtures, and a nematic “island” and SmA phase in the other mixture, were measured in the frequency range from 1?Hz to 10?MHz at different temperatures. The transition temperatures obtained from the polarizing microscope and differential scanning calorimeter measurements agree well with the dielectric relaxation data.