Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Phase diagrams of liquid helium mixtures and metamagnets: Experiment and mean field theory

The phase behavior at low temperature, in particular the critical and tricritical properties, of liquid ³He⁴He mixtures and certain types of metamagnets — a class of highly anisotropic antiferromagnets, such as FeCl₂ etc. — is investigated. Since both systems exhibit two successive phase transitions, one of which is a λ-type of transition while the other is a first order transition, special attention is given to the similarity in the behavior of the two systems. In part A first the experimental and earlier theoretical work are briefly reviewed. Then the phase behavior of each system is calculated on the basis of a simple model treated in mean field approximation. The results obtained are in general qualitative agreement with experiment. For the helium mixtures an isotopic mixture of hard-spheres following Fermi and Bose statistics is used, while for the metamagnet a two sublattice spin $\text{1}\text{2}$ Ising model with nearest neighbor and next-nearest neighbor interactions is employed. A simple physical argument for the analogous behavior of the two models is given. In part B, in an attempt to obtain a deeper understanding of the similarity of the two systems, the Hamiltonians of the two models are extended to include symmetry breaking fields: a particle source field for the helium mixtures and a staggered magnetic field for the metamagnet. The phase diagrams and critical behavior of the two models in an extended thermodynamic space that includes the symmetry breaking fields are discussed in mean field theory.We find that although the two models (treated in the mean field approximation) are very similar, there are differences near T = 0°K and in some of the critical exponents.     

Static critical behavior of 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling

Several Monte Carlo algorithms are used to examine the critical behavior of the 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling for values of the interlayer-to-intralayer exchange ratio R = |′/J| in the interval between 0.01 and 1.0. A finite-size scaling technique is used to calculate the static magnetic and chiral critical exponents α (specific heat), γ and γ_k (susceptibility), β and β_k(magnetization), ν and ν_k(correlation length), and the Fisher exponent η. It is shown that 3D frustrated Heisenberg models on stacked triangular lattice with R > 0.05 constitute a new universality class of critical behavior. At lower R, a crossover from 3D to 2D critical behavior is observed.     

Majority-vote on directed Erd?s-Rényi random graphs

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter q_c, as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.     

Thermal expansivity in superionic RbAg4I5

We have measured the length of a RbAg₄I₅ crystal in the temperature range between 130 K and 300 K using a fused silica LVDT dilatometer system. The expansivity is a smooth, nearly linear function of temperature. There is no anomaly such as a kink, discontinuity, or critical behavior at T_c = 209 K where the superionic β to superionic α phase transition occurs.     

Dynamic critical scattering near the smectic-A—nematic phase transition in CBOOA

High resolution neutron quasielastic scattering has been applied to a study on the critical dynamics near the smectic-A—nematic phase transition in CBOOA. A line narrowing is observed for a certain value of the momentum transfer. We interpret this narrowing as a critical slowing down of the smectic order parameter fluctuations near the transition temperature T_SN. The relaxation times vary between 10^-8 and 10^-7 sec for a temperature interval of 2 K below T_SN.     

Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained models, which are in turn relevant for the study of glass and jamming transitions. We show that for generic tilings there exists a BP transition at a nontrivial critical density, 0<ρ _c <1. Thus, despite the presence of loops on all length scales in hyperbolic lattices, the behavior is very different from that on Euclidean lattices where the critical density is either zero or one. Furthermore, we show that the transition has a mixed character since it is discontinuous but characterized by a diverging correlation length, similarly to what happens on Bethe lattices and random graphs of constant connectivity.     

Anomalous critical behavior of NaV2O5

The temperature dependences and critical behavior of the dielectric constant were studied in NaV₂O₅ along the c axis in a frequency range of 1 MHz-1GHz and a temperature range of 4.2–300 K. An analysis of the data obtained, along with literature data on the heat capacity, magnetic losses, and the ultrasound velocity, indicates that the various physical quantities demonstrate similar temperature dependences in the vicinity of the transition, which corroborates the conclusion on the universality of the critical behavior in NaV₂O₅. Deviations from the predictions of the standard theory of second-order phase transitions were found, such as the asymmetry of the critical behavior above and below the transition and the presence of an anomalous base line.     

Critical behavior of dilute electrolyte solutions

A theory of the critical behavior of a dilute ionic solution is constructed. An expression for the susceptibility in a wide temperature range is obtained. It is shown that ionic solutions belong to the universality class of the Ising model. The Ginzburg parameter of the ionic solutions decreases with the increase of the solvent concentration. In the general case, the critical exponent of susceptibility nonmonotonically depends on the temperature in the crossover region from the Ising-like to the mean-field behavior. In the vicinity of the transition point, the Debye-Hückel screening radius is proportional to the correlation length. As T→T _c, the screening radius tends to infinity and the screening disappears. The voltage between the two phases of the ionic solution is proportional to the order parameter and changes as |T/T _c?1|^β in the vicinity of the phase transition point.     

Absorbing phase transition in energy exchange models

We study energy exchange models with dissipation (λ) and noise (of amplitude σ) and show that in presence of a threshold these models undergo an absorbing phase transition when either dissipation or noise strength or both are varied. Using Monte Carlo simulations we find that the behaviour along the critical line, which separates the active phase from the absorbing one, belongs to directed percolation (DP) universality class. We claim that the conserved version with λ = 1 and σ = 0 also shows a DP transition; the apparent non-DP behaviour observed earlier is an artifact of undershooting in the decay of activity density starting from a random initial condition.     

A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude η_c at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. η^LC_C<η^F_C. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.     

The Si(111) 7 × 7 TO “1 × 1” transition

We have made a detailed study of the Si(111) 7 × 7 to “1 × 1” transition at 1140 K using low-energy electron diffraction. Excess diffuse scattering appears during the transition whose temperature dependence and magnitude are consistent with the loss of the 7th order superlattice intensities showing the transition is to a disordered surface phase rather than a true unreconstructed ×1. This strongly favors the class of models for the 7 × 7 selvedge involving an ordered arrangement of subunits like vacancies or adatoms rather than models with periodic distortion. The superlattice intensity shows the transition is continuous and reversible at least for temperatures below 0.995 T_c. The critical exponent for the long-range order is β = 0.11 ± 0.015 similar to those for 2D Ising or Potts models. However, the system does not show the critical scattering properties expected for simple models. The relaxation time seems to diverge near T_c but only for negative temperature increments.     

High pressure phase transition in PbSnTe

The high pressure structural phase transition in the alloy series Pb_{1 ? x}Sn_xTe has been investigated using resistivity and Hall coefficient measurements. With increasing of tin content the critical pressure decreases linearly and the phase transition becomes less drastic. The anomalous behavior of the resistivity in the phase transition region is explained by band structure changes. It is suggested that the high pressure phase transition in Pb_{1 ? x}Sn_xTe is a metallic-covalent transition.     

Simulations of the chain length dependence of the melting mechanism in short-chain n-alkane monolayers on graphite

The melting transition in solid monolayers of a series of short-chained n-alkanes, n-octane (n-C₈H₁₈), n-decane (n-C₁₀H₂₂), and n-dodecane (n-C₁₂H₂₆) physisorbed onto the graphite basal plane are studied through use of molecular dynamics simulations. Utilizing previous experimental observations of the solid phase behavior of these monolayers, this study investigates the temperature dependence of the phases and phase transitions in these three monolayers during the solid-fluid phase transition, and compares the observed melting behavior to previous studies of hexane and butane monolayers. In particular, this study seems to indicate a greater dependence of the melting transition on the formation of gauche defects in the alkyl chains as the chain length is increased. In light of the previously proposed “footprint reduction” mechanism and variations where the formation of gauche defects are energetically negated, simulations seem to suggest that decane and dodecane monolayers are generally equally as dependent upon the formation of gauche defects for the melting transition to take place, whereas octane monolayers seem to have less dependence, but follow a trend that is established in previous studies of melting in butane and hexane monolayers. Also, the phase transition from a solid herringbone phase into an orientationally ordered “intermediate” phase is found to exhibit some differences as compared to a recent study of hexane monolayers, which may be interpreted as originating from the greater influence of gauche defects. Comparison to experimental melting temperatures is provided where possible, and applications involving thin film manipulation and lubrication is discussed.     

Magnetic Phase Transitions in Nanoclusters and Nanostructures

New phenomena – the first order magnetic phase transitions were observed in nanoclusters and nanostructures. For isolated ferrihydrite nanoclusters (d ～ 1–2 nm) in porous materials, for α-,γ-Fe₂O₃ nanoclusters (d ～ 20–50 nm) and for composites of nanostructured metallic Eu with additives of α-, γ-Fe₂O₃ nanoclusters and adamantane the critical temperatures (T _C, T _N) and magnetic cluster critical sizes (R _cr) were determined by means of thermodynamic models and Mössbauer spectroscopy. The first order magnetic phase transitions (jump-like) proceed by such a way when magnetization and magnetic order disappear by jump without superparamagnetic relaxation. According to thermodynamic model predictions the cluster and interface defects were suggested to play the main role in magnetic behavior. Thus, for the defective α-, γ-Fe₂O₃ nanoclusters, at R ≤ R _cr, the presence of the first order (jump-like) magnetic phase transition was described in terms of magnetic critical size of cluster. The action of high pressure (up to 2 GPa) with shear (120–240°) was effective for defect generation and nanostructure formation. For nanosystems including iron oxide nanoclusters, adamantane and metallic europium and subjected to shear stress under high pressure loading the critical value of defect density was estimated by the study of the character of magnetic phase transition. First-to-second-order (nanostructured metallic Eu) and second-to-first-order (α-, γ-ferric oxide nanoclusters) changes of the character of magnetic phase transition were shown to accompany by the variation of critical temperatures compared to the corresponding bulk values.     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Critical behaviour in the shear elasticity of adamantane in the plastic phase

The elastic constants of the molecular crystal adamantane (C₁₀H₁₆) have been measured at 10 MHz as a function of temperature in the cubic plastic phase, with special attention given to the region just above the order-disorder transition into the tetragonal rigid phase. Both the velocity and attenuation of the C′ shear wave exhibit incipient critical behavior near this transition. The C′ stiffness also shows a pretransitional softening when this transition is approached by increasing the pressure along several isotherms.     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

Electric field induced phase transition in first order ferroelectrics with large zero point energy

An electric field induced phase transition in first order ferroelectrics with very large zero point energy is studied on the framework of the effective field approach. It is well known that when the zero point energy of a system is relatively large, the ferroelectric behaviour is depressed and no phase transition can be observed. The critical value Ω_cf of zero point energy for whom the phase transition disappears turns out to be dependant on the order of transition. For zero point energies larger than this critical value, a phase transition may be induced applying an external electric field. This temperature dependence of the induced polarization shows a discontinuous step when the applied electric field is weak, but becoming a continuous one at a strong applied electric field. Another critical value of zero point energy Ω_cp>Ω_cf is deduced for which no phase transition at all can be attained.     

Spin-lattice relaxation in the rotating frame and extreme slowing-down at the antiferroelectric transition in copper formate tetrahydrate

The effect on the temperature behavior of the spin-lattice relaxation rates in laboratory and rotating frames in presence of extreme slowing-down of the critical fluctuations in an Ising-type system is discussed. Proton spin-lattice relaxation measurements of T₁ and T_1? in water-deuterated copper formate tetrahydrate are presented. The data shown that the anomalous behavior of the proton T_1? in the neighbourhood of the antiferroelectric phase transition recently observed by Zumer and Pir? in the ordinary crystal cannot be ascribed to the critical slowing-down of the water molecules. A possible interpretation on the basis of a mechanism of creation and annihilation of paramagnetic excitons is discussed.