First-order Line Research Articles

Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions

The phase diagram of the Ising model in the presence of nearest- and next-nearest-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by employing an effective-field theory with finite clusters consisting of a pair of spins. A functional form is also proposed for the free energy, similar to the Landau expansion, in order to obtain the phase diagram of the model. The transition from the ferromagnetic (or antiferromagnetic) phase to the disordered paramagnetic phase is of second order. On the other hand, a first-order transition is obtained from the lamellar phase to the paramagnetic phase, as well as from the lamellar phase to the ferromagnetic (or antiferromagnetic) phase, with the presence of a critical end point. An expected singular behavior of the first-order line at the critical end point is also obtained.

Mixed spin-2 and spin- Blume–Capel model

Abstract The influence of increasing the coordination number q on the phase diagrams of the mixed spin-2 and spin- 5 2 Blume–Capel Ising ferrimagnetic system with two crystal-field interactions, D A for spin-2 and D B for spin- 5 2 , is investigated on the Bethe lattice by using the exact recursion equations. The phase diagrams are obtained for the case with equal crystal field strengths when q = 3 , 4 and 6 on the ( k T / | J | , D / | J | ) planes and for the case with unequal crystal field strengths on the ( k T / | J | , D A / | J | ) and ( k T / | J | , D B / | J | ) planes for various values of D B / | J | and D A / | J | , respectively, for q = 4 and 6. Besides the second-order lines, the model presents three types of first-order phase transition lines; one of them ends on the compensation lines ( q = 3 ), the other one ends at a critical end point ( q = 4 ) and last one terminates at a tricritical point ( q = 6 ) for the case with equal crystal field strengths. In this case we have also observed up to four compensation temperatures when q = 6 . Besides the second-order, tricritical and compensation lines, the system presents two types of the first-order lines one of them ending at a tricritical point and the other one ending at an isolated point when unequal crystal field values are taken.

Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field

We study the phase diagram and multicritical behavior of anisotropic Heisenberg antiferromagnets on a square lattice in the presence of a magnetic field along the easy axis. We argue that, beside the Ising and XY critical lines, the phase diagram presents a first-order spin-flop line starting from T=0, as in the three-dimensional case. By using field theory we show that the multicritical point where these transition lines meet cannot be O(3) symmetric and occurs at finite temperature. We also predict how the critical temperature of the transition lines varies with the magnetic field and the uniaxial anisotropy in the limit of weak anisotropy.

Dynamical First-Order Phase Transition in Kinetically Constrained Models of Glasses

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.

Phase diagram of vortices in high-Tcsuperconductors from lattice defect model with pinning

The theory presented is based on a simple Hamiltonian for a vortex lattice in a weak impurity background which includes linear elasticity and plasticity, the latter in the form of integer valued fields accounting for defects. Within a quadratic approximation in the impurity potential, we find a first-order Bragg-glass, vortex-glass transition line showing a reentrant behavior for superconductors with a melting line near $ H_{c2} $. Going beyond the quadratic approximation by using the variational approach of M\'ezard and Parisi established for random manifolds, we obtain a phase diagram containing a third-order glass transition line. The glass transition line separates the vortex glass and the vortex liquid. Furthermore, we find a unified first-order line consisting of the melting transition between the Bragg glass and the vortex liquid phase as well as a disorder induced first-order line between the Bragg glass and the vortex glass phase. The reentrant behavior of this line within the quadratic approach mentioned above vanished. We calculate the entropy and magnetic induction jumps over the first-order line.

Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T – D x and T – D z space. A new phenomenon of two TCPs is found in T – D x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D x / J becomes larger or (smaller) with the decrease of t x in T – D z space. Some results have not been revealed in previous works.

Micro-Raman analysis of quantum confined crystalline germanium nanowire arrays

Crystalline germanium nanowires have been grown within the pores of tuneable hexagonal mesoporous silica matrices (HMS) using a supercritical inclusion phase technique. Micro-Raman spectroscopical analysis was performed on the Ge nanowires with diameter ranging from 20 to 85 A. No stress-induced lattice parameter change of the Ge core was detected and the profile and shape of the Raman peak is mainly attributed to the quantum confinement of optical phonons in the Ge nanowires. The physical dimension of the scattering crystalline nanowires lead to a downshift and broadening ofthe first-order Raman line through a relaxation of the q ∼ 0 selection rule.

Resonance Raman spectra of polyyne molecules C 10H 2 and C 12H 2 in solution

Resonance Raman spectra of hydrogen-capped linear carbon molecules, polyynes H(–C C–) n H ( n = 5,6), were measured in n-hexane. For C 10H 2, the peaks at 2123 cm −1 and 2017 cm −1 were identified as the ν 3( σ g) and ν 4( σ g) modes in D ∞h symmetry, respectively. For C 12H 2, the peaks of ν 3( σ g) at 2097 cm −1 and ν 4 ( σ g) at 2053 cm −1 were identified. The relative intensities of the first-order Stokes lines and their resonance enhancement are discussed in terms of the Franck–Condon overlap and resonance absorption relevant to the fully-allowed electronic transition of 1 Σ u + ↔ X ∼ 1 Σ g + .

The critical and compensation temperatures for the mixed spin- [formula omitted] and spin-2 Ising model

The critical and the compensation temperatures of the mixed spin- 3 2 and spin-2 Ising ferrimagnetic system is examined on the Bethe lattice by using the exact recursion equations. First, the ground state phase diagram of the system at zero temperature is obtained on the ( D A / q | J | , D B / q | J | ) plane. Then in order to investigate the influences of the sublattice crystal fields at higher temperatures, the phase diagrams on the ( kT / | J | , D A / | J | ) and ( kT / | J | , D B / | J | ) planes are-calculated for given values of D B / | J | for spin-2 and D A / | J | for spin- 3 2 , respectively. Besides the second-order phase transition lines, two types of the first-order lines one ending at a tricritical point and the other at an isolated critical point are found. The model also exhibits up to four compensation temperatures for appropriate values of the system parameters. The calculations are carried out for the coordination number q = 3 corresponding to the honeycomb lattice.

Velocity-depth trends in Mesozoic and Cenozoic sediments from the Norwegian Shelf: Reply

Sonic velocity, density, and resistivity log data from 60 wells on the Norwegian Shelf have been used to investigate velocity-depth trends in sedimentary rocks as a function of sediment composition, porosity, pore-pressure, burial-history, and compaction processes. A first-order linear velocity-depth trend line has been estimated from published velocity data. The data analyzed in this study, however, show significant variations from this trend line, indicating that no general velocity-depth function can be used when performing more accurate analyses like depth conversion of seismic data, pore-pressure prediction, or basin modeling. Lower Tertiary smectitic sediments from the northern North Sea and Haltenbanken are characterized by relatively low velocities compared to the overlying Pliocene and Pleistocene sediments, causing a distinct velocity inversion. A significant velocity increase at a burial depth corresponding to 70–100C was found and may reflect the alteration of smectite to illite and the initial precipitation of quartz cement in both sandstones and shales. Overpressured Jurassic sediments from Haltenbanken have lower velocities than equivalent hydrostatically pressured sequences but no significant porosity difference. The reduced velocities may be a direct response to lower effective stresses and, thus, reduced elastic compaction. Low velocities in source rocks are mainly attributed to the relatively soft kerogen and resulting velocity anisotropy. The high velocity/depth ratio of Barents Sea sediments (after correcting for Tertiary exhumation) is explained by the burial history of the area, the subsequent thermal exposure of the sediments over time, and thus, the amount of quartz cementation.

Role of isospin in the nuclear liquid–gas phase transition

We study the thermodynamics of asymmetric nuclear matter using a mean-field approximation with a Skyrme effective interaction, in order to establish its phase diagram and more particularly the influence of isospin on the order of the transition. A new statistical method is introduced to study the thermodynamics of a multifluid system, keeping only one density fixed, the others being replaced by their intensive conjugated variables. In this ensemble, phase coexistence reduces to a simple one-dimensional Maxwell construction. For a fixed temperature under a critical value, a coexistence line is obtained in the plane of neutron and proton chemical potentials. Along this line, the grand potential presents a discontinuous slope, showing that the transition is first order except at the two ending points where it becomes second order. This result is not in contradiction with the already reported occurrence of a continuous transformation when a constant proton fraction is imposed. Indeed, the proton fraction being an order parameter in asymmetric matter, the constraint can only be fulfilled by gradual phase mixing along the first-order phase-transition line, leading to a continuous pressure.

Long-Range Geoid Testing by GPS-Leveling Data in Turkey

A long-range geoid testing procedure is presented using a geometrical geoid profile, which extends in an approximate north–south direction between the Mediterranean and the Black Sea. Along the first-order leveling line of the Turkish National Vertical Control Network (TNVCN), 47 leveling benchmarks at 20–25 km intervals were selected as global positioning satellite (GPS)-leveling control points with known Helmert orthometric heights. The geometrical geoid profile computed from GPS-leveling data was compared with the national Turkish Geoids 1991 (TG91) and 1999A (TG99A), and global geoids OSU91A and EGM96. In absolute geoid testing, it is verified that TG91 has a tilt and bias with respect to the GPS-leveling geoid. TG99A, which has no tilt and bias, displays the root mean square agreement of ±12 cm in the north–south direction. In relative geoid testing, it is understood that TG91 can only be used at 25 km or shorter baseline lengths, whereas TG99A can be used over all baseline lengths with an accuracy t...

Influence of high-resolution processing on background noise distribution in ship-borne radar

When a high-resolution algorithm is applied in a ship-borne radar, its non-linearity and distributional characteristics before high-resolution processing determine the distributional characteristics of background clutter after high resolution and detector design afterwards. Because background noise before high-resolution has physical significance, the statistical model of first-order Bragg lines and second-order components of sea clutter is put forward. Then, by using higher order cumulative quantity's statistical verification of actual measured data, it is concluded that the background noise before high resolution conforms to normal distribution in a ship-borne radar. The non-linearity of the high-resolution algorithm means that the background noise after high-resolution processing conforms to non-normal distribution. Non-normal-distributed clutter mainly includes Weibull, lognormal, and K-clutter. Rayleigh clutter can be seen as a special case of Weibull clutter. These clutter types have different statistical characteristics and can be discriminated by recognition of clutter characteristics. The numerical domain's distribution after high-resolution processing is determined by an improved, minimum entropy, clutter characteristics recognition method based on the AIC rule, namely, a two-parameter domain-scanning method. This identification method has a higher recognition rate. It is verified that the background noise after high-resolution by pre-whitened-constrained-MUSIC conforms to lognormal distribution.

Multicritical behaviors of the antiferromagnetic Blume–Emery–Griffiths model with the external magnetic field on the Bethe lattice

The antiferromagnetic Blume–Emery–Griffiths model in an external magnetic field is studied by using the exact recursion relations on the Bethe lattice for arbitrary values of biquadratic and for negative values of bilinear interactions. We have studied the thermal variations of two-sublattice magnetizations belonging to spin-1 BEG model to obtain the phase diagrams on the ( H / | J | , kT / | J | ) plane. As a result, we have found that the system presents second- and first-order phase transitions, therefore, tricritical points for appropriate values of K / | J | , D / | J | and q. We have also found that the second-order phase transition lines exhibit reentrant phenomena in temperature, besides it also shows reentrant phenomena for the first-order phase lines in external magnetic field for q = 4 and 6.

Steady states of a nonequilibrium lattice gas

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.

Resonant Raman study of confined Se single helix and Se8 rings

Electron-phonon coupling in Se species confined in the nanoporous matrix has been investigated by using resonant Raman spectra performed with several different laser lines from deep blue to near infrared. The spectra strongly depend on the energies of the excitation laser lines. The one-phonon symmetric A1 modes for Se single helix and Se8 rings are enhanced in the vicinity of their absorption bands. Detailed analysis shows that the Raman band in the high-frequency range of 450–550cm−1 is composed of three individual second-order Raman bands for the confined Se species. These two-phonon Raman shifts occur at twice the frequency shift of the first-order Raman lines, and their intensities are also enhanced when the excitation laser energy matches an electronic transition in Se nanospecies.

Preparation and Characterization of Boron-Doped Diamond Powder: A Possible Dimensionally Stable Electrocatalyst Support Material

Electrically conducting diamond powder was prepared by coating insulating diamond powder ( diam, ) with a thin boron-doped layer using microwave plasma-assisted chemical vapor deposition. Deposition times from 1 to 6 h were evaluated. Scanning electron microscopy (SEM) revealed that the diamond powder particles become more faceted and more secondary growths form with increasing deposition time. Fusion of neighboring particles was also observed with increasing growth time. The first-order diamond phonon line appeared in the Raman spectrum at ca. for deposition times up to 4 h, and was downshifted to as low as for some particles after the 6-h growth. Electrical resistance measurements of the bulk powder (no binder) confirmed that a conductive diamond overlayer formed, as the conductivity increased from near zero (insulating, ) for the uncoated powder to after the 6-h growth. Ohmic behavior was seen in current-voltage curves recorded for the 4-h powder between . Cyclic voltammetric i-E curves for and were recorded to evaluate the electrochemical properties of the conductive powder when mixed with a polytetrafluoroethylene binder. At scan rates between 10 and , for both redox systems was high, ranging from 140 to 350 mV, consistent with significant ohmic resistance within the powder/binder electrode. Our results at this point suggest that the resistance is mainly due to poor particle-particle connectivity. Anodic polarization at 1.6 V vs for 1 h (25°C) was performed to evaluate the morphological and microstructural stability of the conductive diamond in comparison with graphite and glassy carbon (GC) powders. The total charge passed during polarization was largest for the GC powder and smallest for conductive diamond powder . SEM images taken of conductive diamond powder after polarization showed no evidence of microstructural degradation, while significant morphological and microstructural changes were seen for the GC powder.

Determination of displacements in the upper Rhine graben Area from GPS and leveling data

The Upper Rhine graben is a north–northeast trending rift system, which belongs to the European Cenozoic rift system. Today, the southern part of the graben is seismically still active. Earthquakes of magnitude 5 have a recurrence time of approximately 30 years. In order to monitor and to determine the displacements in the study area, GPS measurements have been carried out in two campaigns (1999 and 2000), and observations of the available permanent stations have been processed in 2002. Owing to the small size of deformations expected, high accuracy requirements must be met by the GPS processing. In order to achieve these requirements, precise antenna modeling has been introduced into the processing. As expected the short time span has not enabled to detect significant displacements from the GPS measurements. The deformation analysis shows that the horizontal displacement rates do not exceed 1 mm/year, which is compatible with the geological information. Owing to the fact that the accuracy of positioning with GPS for the vertical coordinates is lower than for the horizontal coordinates, the determination of vertical displacements has been carried out using the leveling technique. In the area of Freiburg, first-order and second-order leveling lines have been chosen for the detection of local displacements on the Weinstetten, on the Lehen-Schonberg and on the Main Border Fault (MBF). Some sections of these faults are still active today. Significant vertical displacements have been observed at the Weinstetten fault in the area of Bad Krozingen and on the MBF in Freiburg. The displacement rates (1925–1984) are 0.17±0.01 mm/year and 0.25±0.02 mm/year respectively. The results agree very well with the results of seismotectonic investigations, and show that ongoing displacements can be found on the northern part of the Lehen-Schonberg fault in the vicinity of Eichstetten, and on the MBF in the vicinity of Freiburg.

60-GHz oxygen band: precise broadening and central frequencies of fine-structure lines, absolute absorption profile at atmospheric pressure, and revision of mixing coefficients

The 60-GHz band of 16O 2 was studied at room temperature and at low (up to 4 Torr) and atmospheric pressures. Precision measurement of central frequencies, self-broadening, and N 2-broadening parameters of fine-structure transitions up to N = 27 was performed by use of a spectrometer with radio-acoustic detection (RAD). The measured parameters are compared with GEISA/HITRAN databanks, MPM92, and other known data. An improved set of the oxygen fine-structure spectroscopic constants is obtained. The absorption profile was recorded in the range 45–96 GHz for laboratory air and pure oxygen at atmospheric pressure by use of a resonator spectrometer with noise level of about ± 0.05 dB/km, and used for deducing the first-order line mixing coefficients and for quantitative assessment of second-order mixing effects. A refined set of MPM parameters is derived from the new data and presented here.

Collapse of Charge Order in a Quasi-One-Dimensional Organic Conductor with a Quarter-Filled Band

A charge-ordered insulator, (DI-DCNQI)2Ag, with a quasi-one-dimensional quarter-filled band is metallized by pressure. It was found that the charge order melts into a curious metallic state with cubic-temperature dependence of the resistivity, which implies the unprecedented mechanism of the electron-electron scattering. We constructed the pressure-temperature phase diagram, where the melting line has a tricritical point dividing the second-order line at low pressures and the first-order line at high pressures just before it vanishes.