Hysteresis Phenomenon in Deterministic Traffic Flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic “particle-hopping” traffic flow model being a straightforward generalization to the well known Nagel–Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the “free-flowing” (or “gaseous”) phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the “jammed” (or “liquid”) phase. Between the two critical values each of these phases may take place, which can be interpreted as an “overcooled gas” phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles. This research has been partially supported by Russian Foundation for Fundamental Research and French Ministry of Education grants.     

Phase diagram of a thin film of the Fe<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> alloy with the “bulk” or “planar” magnetoelastic interaction

Concentration-induced reorientation phase transitions in thin magnetic films of FeCo alloys have been investigated taking into account “planar” or “bulk” magnetoelastic interaction. The critical concentrations of Co corresponding to the phase transition points, as well as the types of the phase transitions, have been determined. The phase diagrams have been plotted.     

Thermodynamics of the HMF model with a magnetic field

We study the thermodynamics of the Hamiltonian mean field (HMF) model with an external potential playing the role of a “magnetic field”. If we consider only fully stable states, the caloric curve does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the caloric curve displays a region of negative specific heat in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions similar to the “gravothermal catastrophe” and to the “isothermal collapse” of self-gravitating systems. In the present case, they correspond to the reorganization of the system from an “anti-aligned” phase (magnetization pointing in the direction opposite to the magnetic field) to an “aligned” phase (magnetization pointing in the same direction as the magnetic field). We also find that the magnetic susceptibility can be negative in the microcanonical ensemble so that the magnetization decreases as the magnetic field increases. The magnetic curves can take various shapes depending on the values of energy or temperature. We describe first order phase transitions and hysteretic cycles involving positive or negative susceptibilities. We also show that this model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking.     

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”) of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”) analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A₈₀B₂₀ , a ternary model system with components “A”, “B”, and “C” in ratios of A₈₈B₇C₅ (as in Al₈₈Y₇Fe₅ , and to atomic coordinates in a Zr₈₀Pt₂₀ system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.     

Effect of the electric field on “incommensurate-commensurate” magnetic phase transitions in BiFeO3-type multiferroics

The specific features of the “incommensurate-commensurate” phase transitions induced by a magnetic field in multiferroics (materials with coexisting magnetic and electric ordering) are considered. These materials are ferroelectromagnets, for example, bismuth ferrite BiFeO₃ and BiFeO₃-based compounds, which have spatially modulated spin structures. It is shown that the interaction between the electric and magnetic subsystems of the multiferroic material can lead to an electric-field-induced shift of the critical magnetic field corresponding to the transition from a spatially modulated state to a homogeneous antiferromagnetic state. According to the theoretical estimates obtained for material parameters characteristic of the bismuth ferrite, this shift is of the order of 0.5 T in an electric field of 50 kV/cm. The phase diagrams are constructed in the “electric field-magnetic field” coordinates. The results of calculations performed in the harmonic incommensurate structure approximation are compared with the exact soliton solution.     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Progress and bottlenecks in simulating lattice gauge theory with fermions

We present a progress report in lattice gauge theory computer simulations which includes the effects of light, dynamical fermions. Microcanonical and hybrid microcanonical-Langevin alogrithms are presented and discussed. A method for “accelerating” stochastic differential equations and defeating critical slowing down is reviewed. Physics applications such as the thermodynamics of quantum chromodynamics, hierarchal energy scales in unified gauge theories, and the phase diagram of theories with many fermion species are discussed. Prospects for future research are assessed.     

Ground-state instability in systems of strongly interacting fermions

The stability of a fermion system is analyzed for a model repulsive pair interaction potential. The possibility of different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analyticity properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, but instead belongs to the class of topological transitions. A phase diagram constructed for this model in the variables “screening parameter-coupling constant” displays two kinds of topological transitions: a “5/2” kind, similar to the known Lifshitz transitions in metals, and a “2” kind, characteristic for a uniform strongly interacting system. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 893–899 (25 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Relaxation processes in the incommensurate phase of a crystal with defects

The nature of the relaxation of the incommensurate superstructure of a ferroelectric to the equilibrium state is investigated experimentally. It is shown that near a phase transition the temperature dependence of the relaxation time of the incommensurate phase of the defective crystal is exponential. This law agrees qualitatively with the notion of domain wall motion in an inhomogeneous medium containing “random local phase-transition temperature” type defects. Fiz. Tverd. Tela (St. Petersburg) 41, 513–515 (March 1999)     

Distribution of Overlap Profiles in the One-Dimensional Kac--Hopfield Model

We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature. In the thermodynamic limit we obtain large deviation estimates for the distribution of the “local” overlaps, the range of the interaction, , being the large parameter. We show in particular that the local overlaps in a typical Gibbs configuration are constant and equal to one of the mean-field equilibrium values on a scale . We also give estimates on the size of typical “jumps”, i.e. the regions where transitions from one equilibrium value to another take place. Contrary to the situation in the ferromagnetic Kac-model, the structure of the profiles is found to be governed by the quenched disorder rather than by entropy. Received: 14 February 1996 / Accepted: 30 September 1996     

Spin ice in a field: Quasi-phases and pseudo-transitions

Thermodynamics of a short-range model of spin ice magnets in a field is considered in the Bethe-Peierls approximation. The results obtained for [111], [100], and [011] fields agree reasonably well with the existing Monte Carlo simulations and some experiments. In this approximation, all extremely sharp field-induced anomalies are described by analytic functions of temperature and the applied field. In spite of the absence of true phase transitions, the analysis of the entropy and specific heat reliefs over the H-T plane allows discerning “pseudo-phases” with a specific character of spin fluctuations and defining the lines of relatively sharp “pseudo-transitions” between them.     

On the Study of Jamming Percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a “No Parallel Crossing” rule for the TBF proof of a glassy transition to be valid. Furthermore, most knights-like models fail a “No Perpendicular Crossing” requirement, and thus need modification to be made rigorous. We also show how the “No Parallel Crossing” requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.     

Search for signatures of phase transition and critical point in heavy-ion collisions

The general concepts in the critical phenomena related with the notions of “scaling” and “universality” are considered. Behavior of various systems near a phase transition is displayed. Search for clear signatures of the phase transition of the nuclear matter and location of the critical point in heavy-ion collisions (HIC) is discussed. The experimental data on inclusive spectra measured in HIC at RHIC and SPS over a wide range of energies s _{N N} ^1/2 = 9–200 GeV are analyzed in the framework of z-scaling. A microscopic scenario of the constituent interactions is presented. Dependence of the energy loss on the momentum of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions described in terms of momentum fractions is used to characterize the nuclear medium by “specific heat” and colliding nuclei by fractal dimensions. Preferable kinematical regions to search for signatures of the phase transition of the nuclear matter produced in HIC are discussed. Discontinuity of the “specific heat” is assumed to be a signature of the phase transition and the critical point.     

A thermodynamic multiphase scheme treating polymer crystallization and melting

A comparison of transition and melting temperatures of n-alkanes with experimentally determined ticknesses and melting points of polyethylene lamellae shows that the variation of the thickness with the crystallization temperature virtually agrees with the chain length dependence of the crystalline-mesomorphic phase transition in n-alkanes. Mesomorphic polyethylene layers are stable objects up to the thickness set by this phase transition. The findings lend further support to the view that polymer crystallization generally uses a route which includes a passage via a mesomorphic phase. We construct a thermodynamic scheme dealing with the transitions between melt, mesomorphic layers and lamellar crystallites, assuming for the latter ones that they exist both in an initial “native” and a final “stabilized” form. Application of the scheme in a reconsideration and quantitative evaluation of SAXS and DSC results previously obtained for PE, sPP, iPS and P(epsilonCL) yields the equilibrium transition temperatures between the various phases, latent heats of transition and surface free energies. According to the results the mesomorphic phases are not liquid-like, but have thermodynamic properties which place them truly intermediate between melt and crystals.     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Phase diagram of a 2D Ising model within a nonextensive approach

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for q ≠ 1. A q - phase diagram (critical temperature vs. the entropic parameter q) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index q. It is shown that such phases favors some energy levels of magnetization states. It is also shown that the contribution of the Tsallis cutoff is capital to the existence of phase transitions.