Phase transitions in the Ising model with transverse field

We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.     

Phase transitions and relaxation characteristics of Quantum Magnets and Quantum Glasses

An overview is presented of the phase changes as well as certain relaxation characteristics of model quantum magnets, magnetic glasses and proton glasses. Although the systems considered are quite varied, they are connected by the common themes of tunneling, transverse Ising model, long-ranged interactions and above all, the occurrence of quantum phase transitions. Because the interactions are long-ranged, mean-field theory is eminently suitable for analyzing both the equilibrium and nonequilibrium properties. Wherever pertinent, detailed comparisons with experimental data have been presented.     

Existence and Order of the Phase Transition of the Ising Model with Fixed Magnetization

Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed magnetization when crossing the boundary of the coexistence region. Modifications of this result for systems of spatial dimension greater than two are discussed.     

Equilibrium Phase Transitions in Coupled Map Lattices: A Pedestrian Approach

A class of piecewise linear coupled map lattices with simple symbolic dynamics is constructed. It can be solved analytically in terms of the statistical mechanics of spin lattices. The corresponding Hamiltonian is written down explicitly in terms of the parameters of the map. The approach follows the line of recent mathematical investigations. But the presentation is kept elementary so that phase transitions in the dynamical model can be studied in detail. Although the method works only for map lattices with repelling invariant sets some of the conclusions, i.e., the role of local curvature of the single site map and properties of the nearest neighbour coupling might play an important role for phase transitions in general dynamical systems.     

Absence of first-order phase transitions for antiferromagnetic systems

We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.     

Analytical Approach for Piecewise Linear Coupled Map Lattices

A simple construction is presented which generalizes piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. In particular, the spin Hamiltonian which is generated by the symbolic dynamics is accessible. As an example, a formal relation between a globally coupled system and an Ising mean-field model is established. The phase transition in the limit of infinite system size is analyzed and analytical results are compared with numerical simulations.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Phase transition for Ising frustration potentials

A frustration potential is a sum of interactions the terms of which are not simultaneously minimized even in the ground-state spin configurations. Ising models with such potentials can be discussed by the use of contours. The Peierls condition for the phase transition can be properly generalized, taking into account the presence of zero-energy contours. Frustration has some special features in two dimensions, which we study in detail. The connection with models of spin-glasses is discussed.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.     

Dynamic phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

The stationary states of the kinetic spin-1 Blume-Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and crystal field (D) interactions. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. It is found that the magnetization oscillates around nonzero values at low temperatures (T) for the ferromagnetic (F) phase while it only oscillates around zero values at high temperatures for the paramagnetic (P) phase. There are regions of the phase space where the two solutions coexist. The dynamic phase diagrams are obtained on the (kT/J,h/J) and (kT/J,D/J) planes for the coordination number q=4. In addition to second-order and first-order phase transitions, dynamical tricritical points and triple points are also observed.     

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian Hi of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomena occur when the value of the transverse field is not zero and the reentrant diagram is given.     

Phase diagram of the half-infinite ising model

The phase diagram is analyzed rigorously, and in particular the wetting transition is discussed.     

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian H_i of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomenaoccur when the value of the transverse field is not zero and the reentrantdiagram is given.     

Phase transitions in sol-gel derived Eu-doped PZT ceramics

Polycrystalline samples of Pb_1-z Eu _z (Zr_0.60Ti_0.40)_1-z/4O₃ (z = 0.07, 0.08 and 0.10) (abbreviated as PEZT) were prepared through the metal-alkoxide sol-gel route. X-ray diffraction analysis indicates that the PEZT compounds (nearly single phase) or solid-solution can be formed at 500°C through this route. The pellet samples sintered at 1300°C for 7 h have high density. SEM study shows the uniform distribution of spherical grains on the sample surface. Detailed dielectric studies of the compounds as a function of temperature (30–450°C) at two frequencies (10³ and 10⁴Hz) show that the broadening of the permittivity peak and transition temperature depend on Eu-ion concentration. Analysis of diffusivity (γ) of the dielectric peaks of the crystals provides its value between 1 and 2, indicating the different degrees of substitution disordering in the system. The values of remanent polarisation and coercive field decrease with increase in Eu concentration.     

Ising Quantum Chain and Sequence Evolution

A sequence space model which describes the interplay of mutation and selection in molecular evolution is shown to be equivalent to an Ising quantum chain. Observable quantities tailored to match the biological situation are then employed to treat three fitness landscapes exactly.     

Phase transitions in the Ashkin-Teller model

For some values of the coupling constants, a proof of the existence of two phase transitions in the Ashkin-Teller model is given. Only correlation inequalities are used.     

Phase transitions driven by quasiparticle interactions

After a survey of the solid–liquid transition, driven by phonon–phonon interactions, attention is next focussed on two phase transitions caused by electron–phonon interactions. These are (i) the Barden–Cooper–Schrieffer pure metal superconducting transition and (ii) the original Peierls instability. These have closely similar forms for the respective transition temperatures, both being related to energy gaps. Spin–phonon interactions are then discussed in relation to spin-Peierls materials. Finally, magnon–magnon interactions are treated in the context of the ferromagnetic–paramagnetic transition in the itinerant electron systems Fe, Co and Ni. Heuristic and phenomenological arguments, plus of course experiment, provide the basis for the conclusions drawn here.     

A mean—field approximation scheme containing the spatial parameter and its application to a surface—reaction—like cellular automaton model

Using an AB2 Surface-reaction-like cellular automaton model,we present a modified mean-field approximation scheme for describing some dynamic lattice models,in which a lattice freedom parameter N is introduced as a variable,We obtain the phase diagrams of the example model for linear,hexagonal,square and triangular lattices,and we reveal a second-order phase transiton which has not been found using using traditional approaches.     

量子相变

量子相变是一种发生在绝对零度,由量子涨落而非热涨落导致的相变现象,满足著名的海森堡不确定关系。通过零温量子临界点的研究,可获知物质系统更广泛范围的行为,包括稀土磁性绝缘体,高温超导体和二维电子气体等。     

动态外场作用下Ising自旋体系的非平衡动态相变

系统地考察了Ising自旋体系的动力学方程对三种不同性质的驱动外场（正弦波 、方波和锯齿波）的动态响应及其相应的非平衡动态相变特征.在正弦波和方波的驱动场 作用下，体系存在分别对应于低温对称破缺的铁磁有序态和高温对称顺磁无序态的动态非平衡转变，相应的动态转变相界上存在区分连续转变和非连续转变的三临界点；而锯齿波驱动 场情形下体系始终维持对称性破缺的有序态.体系动态转变表现出的上述差异与作用外场的驱动特征有关.确定了表征相应动态相变相界的临界驱动外场振幅h0C和频率 ωc、体系的温度tc, 并给予了分析讨论 关键词： Ising自旋体系 非平衡动态相变 对称性 平均场