CRITICAL SCALING THEORY OF GENERALIZED PHASE TRANSITION AND ITS UNIVERSALITY

Generalized phase transition (GPT) refers to the transition process of material systems from one steady-state to another. It includes equilibrium phase transition (EPT) and nonequilibrium phase transition (NPT), and phase transitions intermediate between them. In this paper some results on the study of critical scaling relations of the NPT and EPT are obtained. We developed the critical scaling theory of EPT and advanced a universal critical scaling theory of GPT. The critical scaling relations(scaling laws) has more niversality. The critical exponents calculated from our theory are identical with the results of experiments and other theories about EPT and NPT systems. Because the basic model of the theory does not depend on the concrete material system, it has a certain unversality. Its results thus can be applied to generlized phase transition systems, such as the electrorheological fluid and magnetorheological fluid systems.     

Gyrotropic and piezoelectric coefficients and attenuation of elastic waves in BaTiO3

Using Landau theory of phase transition, expressions for gyrotropic coefficients and piezoelectric coefficients are obtained for barium titanate in the tetragonal phase. Both coefficients vanish at the ferroelectric phase transition temperature. The piezoelectric coefficients tallied with the literature values. The attenuation coefficients for elastic waves propagating along the principal directions in tetragonal, orthorhombic and rhombohedral phases are derived based on Landau theory. It is predicted that there will be slight amplification for both longitudinal and transverse modes in the rhombohedral phase at a temperature close to the rhombohedral phase transition temperature.     

Monopole production in the very early universe in a first-order phase transition

The implications for magnetic monopole production of a first-order phase transition in the evolution of the early universe are discussed. Because of cosmological limits on the monopole density, strong constraints on the properties of the phase transition are required. The universe is likely to supercool, with the phase transition terminating either because the metastable state becomes unstable or because the universe is filled by “bubbles” of the broken symmetry state. Both scenarios are complicated by the exponential expansion of the supercooled universe, owing to the large cosmological term existing before the phase transition. To achieve the required dilution of the monopole/entropy ratio in either case would require a fortuitous arrangement of the parameters of the grand unified theory. We also comment on the implications of a first-order phase transition for the generation of a baryon excess. In the appendix, we elaborate a conjecture concerning the theory of nucleation in finite-temperature quantum field theory.     

Hydrogen-bond topology and the ice VII/VIII and ice Ih/XI proton-ordering phase transitions

The existence of an ice Ih/XI proton-ordering transition to a low-temperature ferroelectric phase has sparked considerable debate in the literature. Electronic density functional theory calculations, extended using graph invariants, confirm that a transition to a low-temperature ferroelectric phase should occur. The predicted transition at 98 K is in qualitative agreement with the observed transition at 72 K, and the low-temperature phase is the ferroelectric phase determined in diffraction experiments. The theoretical methods used to predict the phase transition are validated by comparing their prediction to the well-characterized ice VII/VIII proton-ordering transition.     

Effects of Quantum Correction on Dynamical Phase Transition in a Single Species Bosonic Josephson Junction

In this paper,by employing Bogliubov backreaction method,we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction.Compared with mean field theory results,we find that the transition point is shifted.The dynamical phase transition is accompanied by a change of the entanglement entropy,which is found to reach a maximum at the transition point of the mean field theory.     

Effects of Quantum Correction on Dynamical Phase Transition in a Single Species Bosonic Josephson Junction

In this paper, by employing Bogliubov backreaction method, we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction. Compared with mean field theory results, we find that the transition point is shifted. The dynamical phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point of the mean field theory.     

Gauge theory picture of an ordering transition in a dimer model

We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3D XY model. The continuous nature of the transition is confirmed by a flowgram analysis.     

Scaling in four-dimensional quantum gravity

We discuss scaling relations in four-dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called “baby universe surgery” we study the critical region of the theory. The position of the phase transition is given with high accuracy and some critical exponents are measured. Their values prove that the transition is continuous. We discuss the properties of two distinct phases of the theory. For large values of the bare gravitational coupling constant the internal Hausdorff dimension is two (the elongated phase), and the continuum theory is that of so called branched polymers. For small values of the bare gravitational coupling constant the internal Hausdorff dimension seems to be infinite (the crumpled phase). We conjecture that this phase corresponds to a theory of topological gravity. At the transition point the Hausdorff dimension might be finite and larger than two. This transition point is a potential candidate for a non-perturbative theory of quantum gravity.     

公度-无公度相变与朗道的相变唯象理论

本文主要介绍晶体中公度-无公度相变。无公度相是结构相变的产物,它与软模概念有着紧密联系。应用朗道的相变唯象理论可以相当好地解释这一相变行为,本文将给予详细综述。基于朗道自由能公式,讨论了无公度相的热力学性质,介电性质和弹性性质,以及杂质和缺陷将影响相变过程,杂质的“钉扎”效应导致各种观察量在相变过程中出现滞后现象。最后,无公度相中的新元激发-振幅子和相位子的色散特性,也从唯象观点作了讨论。主要的理论结果将与有关的实验数据和曲线进行比较,同时指出理论不完善之处以及尚待进一步研究的课题。     

一维有机导体的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls 相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体tetrathiafulvalene-tetracyanoquinodimethane的Peierls相变温度进行了计算.并对其金属-绝缘体相变机制进行了讨论. 关键词： 电子-声子相互作用 Peierls相变温度 一维有机导体     

Failure of mean field theory at large N

We study strongly coupled lattice QCD with N colors of staggered fermions in 3+1 dimensions. While mean field theory describes the low temperature behavior of this theory at large N, it fails in the scaling region close to the finite temperature second order chiral phase transition. The universal critical region close to the phase transition belongs to the 3D XY universality class even when N becomes large. This is in contrast to Gross-Neveu models where the critical region shrinks as N (the number of flavors) increases and mean field theory is expected to describe the phase transition exactly in the limit of infinite N. Our work demonstrates that infrared fluctuations can be important close to second order phase transitions even when N is strictly infinite.     

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.     

PNASE TRANSITION APID CROSSOVER IN LATTICE GAUGE THEORIES

We propose a modified mean field theory for pure Lattice gauge systems. The theory emphasizes independent playuette contributions rather than independent link contributions as in the usual mean field theory. Using only one lihk integrals, the theory reproduces the overall behavior of mean plaquette energies for various gauge groups over a wide range of β including the phase transition or crossover region. The theory discriminates between actual phase transition and crossover behavior for different gauge groups.     

Thermodynamics of the surface of <Superscript>4</Superscript>He crystals

The conditions for applicability of the mean field theory for describing the thermodynamics of the surface of ⁴He crystals are investigated based on analysis of experimental data. It is found that although the faceting phase transition itself is a Berezinsky–Kosterlitz–Thouless phase transition, the thermodynamic potential outside a narrow neighborhood of the transition temperature can be expanded into a series in terms of the Landau theory of second-order phase transitions.     

单模光腔中N个二能级原子系统的有限温度特性和相变

本文研究单模光场中N个二能级原子Dicke模型的有限温度特性和相变. 把原子赝自旋转换为双模费米算符, 用虚时路径积分方法推导出系统的配分函数, 对作用量变分求极值得到系统的热力学平衡方程, 及原子布居数期待值和平均光子数随原子-光场耦合强度变化的解析表达式. 重点研究了在量子涨落起主导作用的低温区, 由耦合强度变化产生的从正常相到超辐射相的相变, 指出该相变遵从Landau连续相变理论, 平均光子数可作为序参数, 零值表示正常相, 大于零则为超辐射相. 在零温极限下本文的结果和量子相变理论完全符合. 另外, 本文也讨论了系统的热力学性质, 比较有限温度相变和量子相变的异同. 发现, 在强耦合区低温稳定态的光子数和平均能量都和绝对零度的值趋于一致, 而超辐射相的熵则随耦合强度的增强迅速衰减为零.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

Phenomenological theory of first-order phase transitions characterized by a one-component order parameter

The Landau theory of phase transitions is generalized with regard to the change Δρ_inv in the charge distribution probability density that does not break the symmetry of the high-symmetry phase. It is shown that the inclusion of Δρ_inv makes it possible to describe first-order phase transitions in terms of a fourth-order non-equilibrium potential. The suggested theory leads to the conclusion that the ferroelastic transition in TeO₂ is a first-order phase transition.     

Pressure dependence of elastic properties of wurtzite ZnO crystal

We present the pressure dependence of elastic properties of the wurtzite phase of ZnO undergoing wurtzite to the rocksalt phase transition. A simple Landau theory is developed to describe the structural phase transition between wurtzite to rocksalt phases observed in ZnO. We have defined the necessary order parameter of the wurtzite to the rocksalt phase transition. We present a detailed analysis of the pressure dependence of the elastic and shear constants of the wurtzite phase of ZnO. The theoretical predictions are in the line with experimental results.     

Asymmetric <Emphasis Type="Italic">c</Emphasis>(4×4) → γ(2×4) reconstruction phase transition on the (001)GaAs surface

The c(4×4) → γ(2×4) reconstruction phase transition on the (001)GaAs surface is studied experimentally. It is shown that it is a first-order phase transition. The phase transition is found to exhibit a highly asymmetric hysteresis. The difference between the direct and inverse runs of the hysteresis is explained in terms of the mean field theory of an adsorption-induced phase transition by the substantial contribution of lateral multiparticle interactions in the adsorbate.     

Supersymmetric cosmology and running masses and coupling constants

We discuss the possibility that the phase transition to the SU(5) asymmetric phase of a supersymmetric grand unified theory occurs without bubble formation, the temperature-dependent mass squared having changed sign. When this phase transition does occur by bubble formation, we study the effect of running coupling constants and masses on the tunnelling rate. The constraints on Higgs scalar masses resulting from the requirement that the theory be asymptotically free are also discussed.