Synergetic model for hysteresis and Re-entrant phase transitions

Summary We propose a very simple synergetic model system in which two subsystems (the state of each of them is described by an order parameter) acted upon by the same driving force interact via a crossed feedback: the input field to a subsystem is coupled to the order parameter of the other one. Each subsystem, if taken alone, exhibits a normal phase transition. The phase plane spanned by the two coupling parameters exhibits at least two relevant regions in which the behaviour of the order parameters is qualitatively different than in the isolated subsystems. The new features introduced by the synergism are, respectively, hysteresis and re-entrancy. We also make two simple examples of applications of the theory using a crude form of mean-field approximation and obtain a good qualitative agreement with experiment. Our synergetic approach shows that hysteresis and re-entrancy have a common origin: the interplay between two order parameters.

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Riassunto Si propone un modello sinergetico molto semplice nel quale due sottosistemi (a ciascuno dei quali è associato un parametro d'ordine) interagiscono, sotto l'azione dello stesso campo, mediante una retroazione incorciata: il parametro d'ordine di ciascun sottosistema modifica l'azione del campo esterno sull'altro sottosistema. Ciascun sottosistema, considerato isolatamente, ha una transizione di fase normale. Il sinergismo introduce delle caratteristiche assenti nei sottosistemi isolati: a seconda dei valori delle costanti di accoppiamento si possono avere transizioni con isteresi o transizioni rientranti. Il modello, applicato a due sistemi reali mediante una rozza forma di approssimazione di campo medio, risulta in buon accordo qualitativo con gli esperimenti. Il nostro approccio sinergetico mostra che isteresi e transizioni rientranti hanno un'origine comune: l'interazione fra due parametri d'ordine.

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Реэюме Мы предлагаем очень простую синергетическю модельную систему, в которой две подсистемы (состояния каждой иэ них описывается с помощяю параметра порядка) вэаимодействуют, при воэдействии того же поля, череэ дерекрестную обратную свяэь: исходное поле для одной подсистемы свяэано с параметром порядка другой подсистемы. Каждая подсистема, рассмотренная отдельно, обнарчживает нормальный фаэовый переход. Фаэовая плоскость, иэмеряемая двумя параметрами свяэи, обнаруживает, по крайней мере, две соответствующие области, где поведение параметров порядка окаэывается количественно раэличным по сравнению с иэолированными подсистемами. Соответственно, синергиэм вводит новуе свойства, отсутствующие в иэолированных подсистемах: в эависимости от величины константы свяэи воэможны переходы с гистереэисом или ?входящие? переходы. Рассматриваются два простых примера применения предложенной теории, испольэуя грубую форму приближения для среднего поля, и получается хорошее количественное согласие с экспериментом. Наш синергетический подход покаэывает, что гистереэис и ?входящие? переходы имеют общее происхождение: вэаимосвяэь между двумя параметрами порядка.

     

Blume–Emery–Griffiths纳米管的热力学与相变性质

利用有效场理论研究了圆柱形纳米管上Blume-Emery-Griffiths系统的热力学与相变性质,得到了系统的磁化强度、磁化率、比热和相图.讨论了四次交换作用与二次交换作用的比值 与晶格场对系统热力学量和相图的影响.研究发现:系统存在三临界点,且三临界点由参数 和晶格场共同决定,即若确定了参数 ,则三临界点所对应的晶格场也能确定.随着参数 的增加,系统出现三临界点时所对应的温度和晶格场也相应增大.     

The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton

The Blume-Emery-Griffiths model is simulated using the cooling algorithm which is improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The simulations are carried out on a simple cubic lattice at K/J = −1.5 in the range of −3.5 < D/J < 0.5, with J and K representing the nearestneighbour bilinear and biquadratic interactions, D being the single-ion anisotropy parameter. The phase diagram characterizing phase transition of the model is obtained. We found different kinds of phase transitions between the ferromagnetic, quadrupolar, staggered quadrupolar and ferrimagnetic phases for K/J = −1.5. In particular, the region of the phase diagram containing a ferrimagnetic phase is explored and compared to those obtained by other methods. The simulations confirm that the ferrimagnetic phase occurs in the narrow interval −3.006 ≤ D/J < −3. This result is in a good agreement with Monte Carlo renormalization group and closer to the cluster variation method result than the mean field approximation result.      

Frustrated Blume-Emery-Griffiths model

A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean . Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically. Received 13 January 1997     

Blume-Emery-Griffiths model on the honeycomb lattice

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian –/kT =J _i,j S _i S _j +Ki,jS _i ² _j ² – _i S _i ² +HS _i subject to the constraintK=–ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e )/ . Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.     

Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Field-induced magnetic phase transitions in the Yafet-Kittel model

The Yafet-Kittel model for a two-sublattice ferrimagnet with an antiferromagnetic exchange interaction in one of the sublattices was developed to describe magnetic-field-induced phase transitions in the isotropic and Ising cases. Depending on the relative values of the exchange parameters of the inter-sublattice interaction and the intra-sublattice interaction in the isotropic case, two types of magnetic phase diagrams with two types of second-order phase transitions are possible: to the noncollinear phase and to the spin-flip phase, and, in the Ising case, three types of magnetic phase diagrams with first-order phase transitions are possible. Fiz. Tverd. Tela (St. Petersburg) 41, 1797–1799 (October 1999)     

Thermodynamics and phase transitions in the Overhauser model

We analyze the thermodynamics of the Overhauser model and demonstrate rigorously the existence of a phase transition. This is achieved by extending techniques previously developed to treat the BCS model in the quasi-spin formulation. Additionally, we compare the thermodynamics of the quasi-spin and full-trace BCS models. The results are identical up to a temperature rescaling.     

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.     

Nonequilibrium quantum phase transitions in the Dicke model

We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of sidebands which allow the circumvention of the no-go theorem which otherwise forbids the occurrence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions.     

Electronic phase transitions in the spinless Falicov-Kimball model

We have studied thedV/dI vs.V characteristics of point contacts between the heavy fermion superconductor URu₂Si₂ and the conventional superconductors Zn and NbTi. Contacts between URu₂Si₂ and Zn do not show Josephson effects; instead Andreev reflection type structures occur, which are related to both, the heavy fermion and the conventional superconductor. In contrast, contacts between URu₂Si₂ and NbTi become superconducting at low currents. A closed-loop setup with two NbTi contacts on URu₂Si₂ showed SQUID oscillations in a small magnetic field. Our data give evidence that the contacts should be described as superconductor/normal/superconductor junctions with a thick normal layer on the URu₂Si₂ side of the contact with proximity induced superconductivity in theN-layer in the case of NbTi. With such a model the occurrence or absence of superconductivity can be explained and also the suppression of Andreev-scattering which is frequently observed for contacts between heavy fermion superconductors and normal metals.     

Kitaev模型与拓扑量子相变

文章通过在一种准一维路径上引入自旋算符的约当-维格纳（Jordan—Wigner）变换，证明了Kitaev自旋模型完全等价于一个不含任何非物理自由度的自由Majorana费米子模型。通过对偶变换，进一步证明了这个系统中存在的量子相变可用非定域的拓扑序参量来描述；并且，这些非定域的拓扑序参量在对偶空间变成为定域的朗道类型的序参量。文章作者的工作揭示了传统的量子相变和拓扑量子相变的内在关系，扩展了朗道二级相变理论的适用范围。     

Kitaev模型与拓扑量子相变

文章通过在一种准一维路径上引入自旋算符的约当-维格纳(Jordan-Wigner)变换,证明了Kitaev自旋模型完全等价于一个不含任何非物理自由度的自由Majorana费米子模型。通过对偶变换,进一步证明了这个系统中存在的量子相变可用非定域的拓扑序参量来描述;并且,这些非定域的拓扑序参量在对偶空间变成为定域的朗道类型的序参量。文章作者的工作揭示了传统的量子相变和拓扑量子相变的内在关系,扩展了朗道二级相变理论的适用范围。     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.