One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk

Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at $T=\infty$ are investigated numerically from the point of view of a phase transition. Branching annihilating random walk of the ferromagnetic domain boundaries determines the steady state of the system for a range of parameters of the model. Critical exponents obtained by simulation are found to agree, within error, with those in Grassberger's cellular automata.Comment: 10 pages, Latex, figures upon request, SZFKI 05/9

Non-equilibrium phase transitions in one-dimensional kinetic Ising models

A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at {\it zero temperature} and nearest neighbour random spin exchanges is further investigated here. By increasing the range of spin exchanges and/or their strength the nature of the phase transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first order tricitical point is located at the Glauber ($\delta=0$) limit. Corrections to mean-field theory are evaluated up to sixth order in a cluster approximation and found to give good results concerning the phase boundary and the critical exponent $\beta$ of the order parameter which is obtained as $\beta\simeq1.0$.Comment: 15 pages, revtex file, figures available at request from [email protected] in postscript format, submitted to J.Phys.

On the nature of different types of absorbing states

We present a comparison of three different types of Langevin equation exhibiting absorbing states: the Langevin equation defining the Reggeon field theory, one with multiplicative noise, and a third type in which the noise is complex. Each one is found to describe a different underlying physical mechanism; in particular, the nature of the different absorbing states depends on the type of noise considered. By studying the stationary single-site effective potential, we analyze the impossibility of finding a reaction-diffusion model in the multiplicative noise universality class. We also discuss some theoretical questions related to the nature of complex noise, as for example, whether it is necessary or not to consider a complex equation in order to describe processes as the annihilation reaction, $A +A \to 0$.Comment: 7 figures, Latex fil

Interface depinning versus absorbing-state phase transitions

According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning model within computational accuracy. In this paper the connection between absorbing state phase transitions and interface pinning in quenched disordered media is investigated. For that, we present a mapping of the interface dynamics in a disordered medium into a Langevin equation for the active-site density and show that a Reggeon-field-theory like description, coupled to an additional non-diffusive conserved field, appears rather naturally. Reciprocally, we construct a mapping from a discrete model belonging in the absorbing state with-a-conserved-field class to a discrete interface equation, and show how a quenched disorder is originated. We discuss the character of the possible noise terms in both representations, and overview the critical exponent relations. Evidence is provided that, at least for dimensions larger that one, both universality classes are just two different representations of the same underlying physics.Comment: 8 page

Rare region effects at classical, quantum, and non-equilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe

Absorbing-state phase transitions in fixed-energy sandpiles

We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

The Inelastic Mean Free Path οf Electrons. Research in Budapest, Warsaw, Wrocław and Clermont-Ferrand. Brief History and New Results

The inelastic mean free path of electrons (IMFP) is an important material parameter for description of electron transport processes in solids. This parameter is particularly useful for quantifying the electron spectroscopies, in particular Auger electron spectroscopy, X-ray photoelectron spectroscopy, electron energy loss spectroscopy and elastic peak electron spectroscopy. In this work, a brief overview of the IMFP determination is presented. Generally, there are two groups of methods to determine the IMFP: (i) calculations using the theoretical model based on the experimental optical data, and (ii) calculations using theory relating the IMFP and the measured probability elastic electron backscattering from solids. Major advances in the development of the second group of methods were made in three laboratories; these advances are reviewed here. The elastic backscattering probability, in absolute or relative units, can be conveniently evaluated from the elastic peak intensity. However, much effort is needed to develop the theory for calculating the IMFP, which typically involves the Monte Carlo simulations of electron trajectories in solids. Presently, this theory and typical procedures of the spectra processing are implemented in the software package EPESWIN developed by Jablonski. In recent years, much attention is devoted to the phenomenon of the electron energy losses in the surface region of solids. Reliability of the theory of elastic backscattering is distinctly improved if this effect is taken into account

Anomalous temperature dependence of isotactic polypropylene α-on-β cross-nucleation kinetics

A particular kind of heterogeneous nucleation, i.e., cross-nucleation, is sometimes observed in polymorphic substances, when a new crystal structure nucleates on the surface of a crystal of a different modification. Here we show a unique and apparently incongruous nucleation behavior in polymorphic isotactic polypropylene (i-PP). The rate of cross-nucleation of the monoclinic α-phase on the trigonal β-phase crystals increases with increasing temperature, in the vicinity of the α-crystals melting point. This behavior is contrary to that of the heterogeneous nucleation kinetics of the same crystal on various solid substrates, and also to the previously reported cases of cross-nucleation rate of other polymorphic systems, both exhibiting the expected decrease with temperature in the same range of undercoolings. i-PP α-on-β cross-nucleation apparently eludes the nucleation theory. The results are explained as a manifestation of a kinetic competition between α-on-β cross-nucleation and growth of β-crystalline seeds, and finally reconciled with the current understanding of nucleation. These new findings indicate that further theoretical efforts are needed to include the cross-nucleation phenomenon in the framework of a comprehensive understanding of polymorphic crystallization. Incidentally, this study highlights the intrinsic limits of the, industrially desirable, promotion of β-phase formation in polypropylene