Possible nonanalytic behavior of Ising models in random fields

The magnetization, M, of dilute Ising ferromagnets with quenched random fields is shown to have accumulation points of poles in each of these fields h_i(at h_i → 0) and in the external uniform field H (at H → -h_i). This occurs for all temperatures for which the nonrandom (zero-field) system has H ≠ 0. If both h_i and -h_i are possible then M is probably nonanalyti c for many values of h_i. This casts doubts on expansions in the random fields.     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

Electric-field-induced unwinding of ferroelectric helix in thin smectic C* layers with soft and rigid anchoring of molecules

The unwinding of a helical structure in thin films of a ferroelectric smectic liquid crystal (LC) by an external electric field has been theoretically studied using a discrete model in which every LC layer is characterized by a two-dimensional vector ξ _i (describing the orientation of molecules) and by the polarization P _i . It is established that the unwinding of the LC helix in thin films significantly differs from the well-known behavior of thick samples. In particular, discrete intermediate states (differing by an integer or half-integer number of turns) are formed in thin films for both weak and strong anchoring of molecules to a substrate surface. The physical factor responsible for this behavior is the presence of near-surface regions with thicknesses below the helix pitch and the corresponding uncompensated polarization.     

Dynamical spin system: Exact solution and mean recurrence time

A model involving a chain of N ≥ 2 spins s_i = ±1, i = 1,…,N, evolvi ng syncronously in discrete time t via a nonlinear, autonomous transformation s_i(t+1) = s_i(t)s_i+1(t), i = 1,…,N−1; s_N(t+1) = s_N(t), is presented. The transformation equations are solved explicitly and the detailed decomposition of state space into ergodic sets is found. On the assumption of equally likely initial states, the mean recurrence time is calculated and its variance is discussed. The model displays a strikingly sensitive dependence on the number of spins, and this is reflected in the “staircase” behavior of the mean recurrence time. Remarks are made regarding the connection between the behavior of the model and the ground states of a related two-dimensional Ising model.     

The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(h_i)=pδ(h_i−h₀)+qδ(h_i+h₀)+rδ(h_i), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), h_i is the random field variable and h₀ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h₀, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

Specific features of thermal resistance of silicon in the temperature range 105–130 K

Careful experimental investigations into the behavior of the thermal resistance of single-crystal silicon are carried out in the immediate vicinity of the temperature of an anharmonicity sign inversion (T _i =121.1 K), where phonon thermal resistance approaches zero. An anomalous positive deviation of the total thermal resistance (W) from the linear part of the temperature dependence with a maximum at 121.1 K is found in the temperature range 105–130 K. The temperature behavior of W in this range indicates that the mean free path of phonons is limited by a characteristic size of structural defects and that its temperature dependence exhibits specific features in the vicinity of T _i . It is established that the character of the temperature dependence of W above and below T _i is different. A linear functional relation between the total thermal resistance and the isobaric thermal strain is revealed at positive and negative anharmonicities of atomic vibrations.     

Soluble renormalization groups and scaling fields for low-dimensional Ising systems

A variety of one-dimensional Ising spin systems, including staggered and parallel magnetic fields, alternating and second neighbor interactions, four-spin coupling, etc., are discussed in terms of renormalization group theory. A continuous range of distinct renormalization groups is constructed in exact closed form, analyzed in detail, and compared with exactly calculated thermodynamic properties. Fixed point linearization yields relevant, irrelevant, and marginal operators. All groups yield identical “critical” behavior (at T = 0) with η = 1, δ = ∞, γ = ν = 2 ? α, and with identical linear scaling fields. A generalization of Wegner's analysis to discrete groups yields explicit power series for the nonlinear scaling fields; these are seen to depend on the particular renormalization group and, hence, are physically nonunique. A planar, multiconnected “truncated tetrahedron” model of effective dimensionality log₂ 3 is analyzed via a dedecoration and star-triangle group revealing highly singular behavior as T → T_c = 0.     

Bonabeau model on a fully connected graph

Numerical simulations are reported on the Bonabeau model on a fully connected graph, where spatial degrees of freedom are absent. The control parameter is the memory factor f. The phase transition is observed at the dispersion of the agents power h_i. The critical value f_C shows a hysteretic behavior with respect to the initial distribution of h_i. f_C decreases with the system size; this decrease can be compensated by a greater number of fights between a global reduction of the distribution width of h_i. The latter step is equivalent to a partial forgetting.     

Dynamics of the random field Ising model

Dynamics of the kinetic Ising model in the presence of static random fields is investigated using a self-consistent method. It is shown that if the interface fluctuations of the low temperature phase are small the system at low temperatures stays in a state without long range order. For this state the spin correlation function 〈S_q(t)S_?q(O)> averaged over all configurations of random fields decays exponentially in time with a single wavevector dependent relaxation time which is finite at the transition temperature T₀ and remains very long below T₀. In the mean field approximation the correlation time at the magnetic Bragg peak and at T₀ scales with the magnitude of the random field as τ∞h^?z_h with z_h = 1 for d = 2 and $\text{z}{}_{\mathrm{h}}\text{=}\text{4}\text{3}$ for d = 3, respectively.     

Fragmentation of the high spin discrete neutron and proton states of209Pb and209Bi

The distribution of the discrete 1h _9/2, 2f _7/2, 1i _13/2 and 2f _5/2 proton states of²⁰⁹Bi and 2g _9/2, 1i _11/2, 1j _15/2 and 2g_7/2 neutron states of²⁰⁹Pb have been obtained within the particle-vibration coupling model calculation and compared with the experimental datas baising on the most recent high resolution stripping reaction on²⁰⁸Pb using 480 MeV¹²C projectile. The optimised shell model energies arising from the core-polarisation effect have profound influence for both the study of the structures of the high spin continuum shell model states of²⁰⁸Pb and stability of superheavy nuclei.     

A kinetic study on pyrolysis of iso-propylcyclohexane: Fuel structure effects of alkylcyclohexane isomers on reaction mechanisms

To reveal insights into the fuel decomposition and combustion mechanisms of alkylcycloalkanes, an intermediate-to-high-temperature pyrolysis investigation of iso-propylcyclohexane (i-PCH) was carried out in a flow reactor at low and atmospheric pressures. The quantitative measurements were accomplished with the aid of synchrotron vacuum ultraviolet photoionization mass spectrometry and the mole fraction profiles of over thirty species were evaluated. A new kinetic model for i-PCH was developed, and the model feasibility was validated by the measured data. Model analyses revealed that the CH₃-dissociation reaction is the most sensitive reaction for the destruction of the fuel, and this reaction together with the hydrogen abstractions on active carbon sites takes the dominance of the fuel decomposition. Due to the low bond dissociation energies (BDEs) of the C-C and C-H bonds in the isopropyl group, the primary decomposition temperatures of i-PCH are lower than those of n-propylcyclohexane (n-PCH). Besides, the isopropyl side-chain structure affects many aspects of combustion characteristics of the fuel involving the initial fuel consumption routes and formation of branched species pool, leading to the enhancement of some hexatomic species and inhibition of aromatics production.     

Local impurity phase pinning and pinning force in charge density waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter h. Specifically the pinning force exhibits a threshold at h=1 with exponent . Our model exemplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made. Received 8 July 1998     

Interaction strength and shape difference for the h9/2 and h11/2 configurations in163Tm

The strongly shape driving πh_9/2[541]l/2^? configuration with α=+1/2 exhibits some anomalous, and so far unexplained, features concerning the crossing frequency, ?ω_c, the aligned angular momentum, i_x, and interaction strength, at the alignment of the first pair of i_13/2 quasineutrons in several odd-Z rare earth-nuclei. The h_9/2[541]1/2^? and h_11/2[523]7/2^? bands have been studied in the stably deformed rare-earth nucleus¹⁶³Tm to investigate these features. A difference in band crossing frequency of ～ 80 keV between the two bands is found. Rotational bands built on these two configurations have been found to cross in the spin range I=25/2–29/2 ?. Theγ-decay pattern between the two bands is established in the crossing region and analysed in terms of a moderate shape difference between them. A theoretical estimate of the size of the interaction strength between the two bands is presented and compared to the experimental value. The observed band structure in¹⁶³Tm is very similar to that of¹⁶⁷Lu which has 2 protons and 2 neutrons in addition. This observation is discussed in relation to the similarity of the yrast bands of the two even-even “core” nuclei¹⁶²Er and¹⁶⁶Yb, for which theγ-transition energies are identical within ～0.2 keV below the vi_13/2 crossing.     

A comparative study of the chemical kinetic characteristics of small methyl esters in diffusion flame extinction

The diffusive extinction limits of a series of methyl ester flames, from methyl formate to methyl decanoate, have been measured in the counterflow configuration. Kinetic and transport effects are decoupled by use of the transport-weighted enthalpy term and reveal that the smaller methyl esters (C₂ to C₄) exhibit unique behavior while methyl esters inclusive and larger than methyl butanoate exhibit similar global reactivity to that of the n-alkanes. In order to interpret the experimental observations, a previous kinetic model for methyl butanoate and methyl decanoate has been extended to encompass the oxidation of the smaller methyl esters. Model rate of production analyses highlight the chemical kinetic specificities of methyl formate, methyl ethanoate, and methyl propanoate, through distinctive fuel reaction channels in methanol elimination, methyl radical production, and H atom production respectively. The similarity of global reactivity among the larger methyl esters and n-alkanes is elucidated based on the formation of formaldehyde and ethylene, which drive indifferently the growth of the radical pool at high temperature, thus the flame oxidation rate is similar at the global level.     

Effect of isomerization of reactant molecules on kinetics characteristics of reactions

Mathematical modeling is used to study the effect of isomerization of the reactant molecules on the kinetic characteristics of the initial stage of a chemical reaction within the framework of three isomerization mechanisms: unimolecular, with the formation of an intermediate, or associate. It is shown that the behavior of the kinetic curves is determined by the mechanism of the isomerization of the reactant molecules. The dependence of the effective rate constant k _ef on the reaction rate constants k _i for the elementary reaction steps and the constants of equilibrium K _i between the isomers is established. The effect of temperature on the isomeric composition is examined.     

Electrical conductivity,diffusion of iron and the defect structure of α-Al2O3: Fe

A detailed defect model is developed for α-Al₂O₃:Fe accounting for conduction and diffusion at high temperatures as a function of iron concentration, oxygen pressure and temperature. This model involves single native and iron defects as well as triplets of (Fe_AlAl_iFe_Al), the latter dominating the defect structure at high Fe concentrations. Diffusion of Fe in A1₂O₃ is attributed to Fe_i^3.. The position of the Fe_Al' level is estimated.     

Dynamics of a stochastically driven Brownian particle in one dimension

We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses slowly toward the second particle, labeled M. The displacements of particle M exhibits a crossover from diffusion to drift at a characteristic time which depends on the rate constants. We show that the positional fluctuation of M exhibits an intermediate crossover regime of subdiffusion separating initial and asymptotic diffusive behavior; this is in agreement with the complete set of Master Equations that describe the stochastic evolution of the model. The intermediate crossover regime can be considerably large depending on the hopping probabilities of the two particles. This is in contrast to the known crossover from diffusive to subdiffusive behavior of a tagged particle that is in the interior of a large single-file system on an unbound real line. We discuss our model with respect to the biological phenomena of membrane protrusions, where polymerizing actin filaments (F) push the cell membrane (M).     

Critical fixed points in discrete hydrodynamics

A discrete-cell formulation of hydrodynamics was recently introduced, which is exactly renormalizable in a certain sense: if one knows the discrete equations of motion for a certain cell size W and discrete time interval τ, one can accurately numerically calculate the equations of motion on the coarser scales 2W or 2τ. These coarsening transformations have previously been investigated for the one-dimensional diffusive system. A line of fixed points was found, parameterized by the (positive) diffusivity D'. In this paper we examine the behavior of the coarsening transformation on the D' = 0 manifold in the space of equations of motion for one-dimensional systems. We find another line of fixed points, this one parameterized by the super-Burnett coefficient D'₃. This corresponds to a Gaussian critical point. The possibility of generalizing this to non-Gaussian (Ising-like) critical points is discussed.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).