Expanding the thermodynamical potential and analysis of the possible phase diagram of deconfinement in the FL model

Deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

关于二级相变中热力学物理量突变的分析与自旋链模拟

理论上对二级相变中热容、体膨胀系数、等温压缩系数三个热力学物理量的变化进行了分析,进而使用自旋链模型的基态能量和von Neumann熵随模型参数变化的突变行为对二级相变中这三个物理量的变化所引起的系统序变进行模拟,得到二级相变中热容、体膨胀系数、等温压缩系数的变化是由于系统内部微观上发生关联序变的结果。     

Micromagnetic imaging to determine the nature of the ferromagnetic phase transition in La(0.7)Ca(0.3)MnO3

There is considerable controversy surrounding the nature of the paramagnetic to ferromagnetic phase transition in La(0.7)Ca(0.3)MnO3. We have used transmission electron microscopy to determine whether the phase transition is first or second order. On warming through the transition point, the ferromagnetic phase retreats from the sample surface as it is replaced by the paramagnetic phase. This coexistence of ferromagnetic and paramagnetic phases indicates a primarily first order transition. However, there is also continuous loss of magnetization which precedes the phase transition. We compare this with the phase transition in nickel, an archetypal second order ferromagnet.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length

By exploiting the unique properties of periodic stratified media we demonstrate simultaneously phase matching and enhancement of the optical field under second order nonlinear interaction. This leads to a second harmonic efficiency growth faster than the fifth power of the structure length, far better than the usual quadratic behavior associated with second order nonlinear effects.     

Probing the material properties and phase transitions of ferroelectric liquid crystals by determination of the Landau potential

The full Landau potential of several, widely varying ferroelectric liquid-crystalline materials has been experimentally determined. Tilt angle and polarisation data is analysed across the SmA to SmC transition for varying applied electric-field amplitudes, allowing the determination of all the coefficients of the generalised Landau model of ferroelectric liquid crystals. The materials investigated encompass different materials, including low-polarisation mixtures to high-polarisation single-component materials. The materials also possess a variation in the order of the SmA to SmC phase transition from strongly first order to strongly second order. The effects of both the polarisation and order of phase transition of the system are discussed with respect to the various terms of the generalised Landau model. Further, the mechanisms behind the difference between a first- and second-order phase transition are discussed with respect to the Landau potential and the second Landau coefficient b .     

Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.     

Change in the order of a martensitic phase transformation by an external field

It is shown on the basis of the Labbé-Friedel model for A₃B compounds that the martensitic phase transformation in Nb₃Sn can be changed from a first to a second order transition by an external stress. The Hamiltonian operator describing the phase transition in an external stress field has been mapped to a spin $\text{1}\text{2}$ Ising model with infinite range interactions showing a second order phase transition. Estimates of the transition temperature and the maximum order parameter are given suggesting new experiments.     

On the possibility of improper antiferromagnetism

It has been shown that a magnetic phase transition of the second order with the tensor order parameter can be accompanied by the appearance of the magnetization of sublattices due to exchange effects.     

Perturbative improvement of the Gaussian effective potential

We improve the Gaussian effective potential by a perturbative expansion up to second order around the mean field solution for the case of the φ⁴-theory in 0+1 and 1+1 dimensions. In 1+1 dimensions, we obtain a second order phase transition in agreement with exact statements.     

Canard轨迹原理

为了精确的求出Canard轨迹的描述方程,提出了一个分段表达的非线性模型,能直接求出一个非线性二阶自治方程的相轨迹方程的解析解,能定量求出Canard轨迹的描述方程和参数条件,可以用两类方程简单描述所有的Canard轨迹. 关键词： 非线性系统 Canard轨迹 弛张振荡     

Coupled m-component fields with cubic anisotropy

The critical behavior at phase transitions of two coupled, m-component systems with cubic anisotropy is studied by a simplified model in which the fluctuations are partially considered. The phase transition could be a new fluctuation-induced first order transition into the anisotropic phase, or a new second order phase transition. Unlike in uncoupled systems, the second order phase transition could be into either the anisotropic or isotropic phase. As expected, upon suppression of fluctuations, all results reduce to those of mean field theory.     

Macroscopic description of the ferromagnetic superconductors

We present an improved analysis of the phase transitions in spin-triplet ferromagnetic superconductors within Ginzburg–Landau theory. We put special emphasis on the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity are possible when compared to other phase transitions. The conditions for the phase transitions and the stability conditions are calculated. On the basis of this model, it is argued that the transition from normal phase to the mixed phase of coexistence is always of first order. It was observed from the theoretical calculations that the transition from the ferromagnetic phase to the coexistence phase can cross over from the first to the second order at the tricritical point.     

Investigation of the relation between compression,relaxation, and end losses in the late phases of theta pinch discharges by means of a two-dimensional MHD computer programme

Chemical model reactions are discussed the steady states of which show the phenomenon of non equilibrium phase transitions. One example shows a phase transition of second order, another one shows a phase transition of first order. If diffusion occurs in the case of first order transition, coexistence of two phases in different domains is possible. For plane boundary layers between the domains the coexistence states are found by a construction analogous to the Maxwellian construction of vapor pressure of a Van der Waals gas. For spherical domains the coexistence dates change similarly as vapor pressure of droplets or bubbles with radius.     

Sound propagation near the tricritical point of FeCl2

The magnetically induced phase transitions, near the tricritical point of FeCl₂ were studied by acoustic velocity measurements. Longitudinal waves propagating along the (100) trigonal axis exhibit a critical shift in the velocity along the second order λ-line and anomalous change at the first order phase transitions. The phase diagram in the plane of temperature and applied magnetic field is constructed near the tricritical point.     

Dye laser statistics and the phase transition

By an analytic examination of the photon probability distribution derived by Schaefer and Willis it is shown that, under the conditions for a second order phase transition, the dye laser statistics may be indistinguishable from those of a conventional laser, despite the presence of the triplet states. Under the conditions for a first order phase transition the statistics change, and for some combinations of parameters the change is manifest in the behavior of the normalized second factorial moment of the photon number. Curves are presented that should be directly verifiable by photoelectric counting experiments.     

Effect of optical purity on the critical heat capacity at the smectic-A-(chiral)-smectic-C transition in an antiferroelectric liquid crystal

High resolution ac calorimetric measurements have been carried out near the smectic-A-chiral-smectic-C phase transition in the antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4(')-octyloxybiphenyl-4-carboxylate (MHPOBC). Data on samples with different optical purities have been analyzed in detail using a renormalization-group expression with corrections-to-scaling terms. The chiral-smectic-C(alpha)-chiral-smectic-C phase transition is first order, while the smectic-A-chiral-smectic-C(alpha) phase transition is second order. A direct smectic-A-chiral-smectic-C phase transition, which occurs in near-racemic mixtures, was found to be quasitricritical and weakly first order. This implies that the smectic-A-smectic-C transition in the racemate locates at a special point where four critical lines intersect.     

Charge-density and order-parameter waves in liquid and solid electrolytes in the vicinity of the critical point

The interaction between a solvent which has a second order phase transition and the solute ions leads to a periodical substructure in the vicinity of the critical point. A Bragg peak for X-ray and neutron scattering is predicted.     

Pion condensation at finite temperature: (II). Simple models including thermal excitations of the pion field

We calculate, in several increasingly complex models, the threshold for charged pion condensation in neutron-rich matter at finite temperature, including effects of thermal excitations of the pion field. The thermal pion excitations have two important effects: first, to modify the phase diagram qualitatively from that predicted by mean field theory, and second, to make the phase transition to a nonuniform condensed state at finite temperature always first, rather than second, order.     

Thermodynamics of the phase equilibrium of multicomponent solid solutions containing nano-sized precipitates of the second phase

Based on the theory of regular solutions, the interphase boundary model for the case of an arbitrary number of components is developed. General relations for the calculation of the phase composition of multicomponent solutions containing nano-sized precipitates of the second phase are derived. By the example of binary and ternary solutions, it is shown that a considerable mutual enrichment of the conjugated phases by atoms of components dissolved in them occurs in the case if precipitates of the second phase are characterized by the sizes of the order of several nanometers.