Ground-State 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 based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/z J-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very smallrange of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.     

Magnetic Phase Transitions in Quantum Ising Model with Annealed Antiferromagnetic Bond Randomness

The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field,.and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.     

Quantum Phase Transitions in <Emphasis Type="Italic">s</Emphasis> = 1/2 Ising Chain in a Regularly Alternating Transverse Field

We consider the ground-state properties of the s = 1/2 Ising chain in a transverse field which varies regularly along the chain having a period of alternation 2. Such a model, similarly to its uniform counterpart, exhibits quantum phase transitions. However, the number and the position of the quantum phase transition points depend on the strength of transverse field modulation. The behaviour in the vicinity of the critical field in most cases remains the same as for the uniform chain (i.e. belongs to the square-lattice Ising model universality class). However, a new critical behaviour may also arise. We report the results for critical exponents obtained partially analytically and partially numerically for very long chains consisting of a few thousand sites.     

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model.     

Amorphization in an Ising nanowire; unconventional effects of a uniformly applied transverse field

The phase diagrams and magnetizations of an Ising nanowire with an amorphization are investigated by the use of the effective field theory with correlations, when a uniformly transverse field is applied perpendicularly to the main axis of the nanowire. Some characteristic behaviors have been obtained in them, such as the two types of reentrant phenomena induced by an applied transverse field.     

Tricritical Points and Reentry in the Quantum Hopfield Neural-Network Model

We examine a quantum Hopfield neural-network model in the presence of trimodal random transverse fields and random neuronal thresholds within the method of statistical physics. We use the Trotter decomposition to map the problem into an equivalent classical random Hopfield-type Ising model and obtain phase transitions between the ferromagnetic retrieval and the paramagnetic phases. The influence of competition between the diluted random transverse fields and the diluted random thresholds on the system is discussed, and some interesting results such as tricritical points and reentrance are analyzed.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in a Random Field

The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.     

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.     

Ising model with a new class of four-spin interactions

The Ising model on a Union-Jack lattice, described by a Hamiltonian with second-neighbor pair-pair, four-spin, infinite-range interactions is considered. The model is solved exactly and the results are compared with MFA predictions. Within the exact treatment two new classes of phase transitions are obtained. The first one includes transitions from a disordered to a metastable, ordered and then to a stable and ordered phase with decreasing temperature. The metastable phase does not appear if the temperature is increased. The second one contains transitions between ordered and partialy ordered, partialy frustrated phases.     

Gaussian random field p-spin-interaction ising model in a transverse field

The Gaussian random field Ising model with p-spin interactions in the presence of a transverse field is studied by combining the Suzuki-Trotter approach and the thermodynamic perturbation theory. The first-order phase transitions are found in the limit p → ∞, in contrast to the cases with p=2.     

Phase Diagram of a Quantum Hopfield Spin Glass with the Pseudo-Inverse Rule

A quantum Ising spin-glass model in a transverse field is presented. The network is based on a modified version of the Hopfield spin glass. The equations for the order parameters describing the ordered phases are obtained, and the phase transitions of the system are analyzed. The ordered phases are suppressed by the existence of both quan turn effects and the random overlaps between the patterns.     

Frustration in a transverse Ising nanoisland: effects of interlayer coupling

The phase diagram and magnetizations in a transverse Ising nanoisland are examined by using the effective field theory with correlations. The nanoisland is constructed from two layers with nine atoms in each which are coupled by the interlayer coupling. We present some characteristic phenomena in them which come from the frustration induced by an interlayer coupling and two transverse fields.     

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.     

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.     

Quantum Hopfield model with a random transverse field and a random neuronal threshold

A quantum Hopfield model with a random transverse field and a random neuronal threshold is investigated by use of the statistical physics method. The Trotter decomposition is used to reduce the problem to that of an equivalent classical random Ising model. Phase transitions between the retrieval phase and the paramagnetic phase are obtained, and the influence of competition between the quantum fluctuations and the random threshold on the possibility of the existence of the ordered retieval phase of the network is considered.     

Trimodal random-field spin- Ising systems in a transverse field

The trimodal random-field spin- Ising system in a transverse field is investigated by combining the pair approximation with the discretized path-integral representation by introducing a parameter p to simulate the fractions of the spins not exposed to the external longitudinal magnetic field. The variation of the critical reduced transverse field and longitudinal magnetic field with the parameter p is studied for different coordination numbers and it is found that the system does not exhibit any tricritical points for p>0.22. The phase diagrams with respect to the external longitudinal random-field and the second-order phase transition temperature are obtained for given values of the transverse field, coordination numbers and the parameter p. It is found that for appropriate values of the system parameters the system does present tricritical points and reentrant phase transitions, which may be caused by the competition between the quantum effects and randomness.     

Dynamic phase transition of ferroelectric nanotube described by a spin-1/2 transverse Ising model

The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.     

Magnetic dipolar ordering and quantum phase transition in an Fe8 molecular magnet

We show that a crystal of mesoscopic Fe(8) single-molecule magnets is an experimental realization of the quantum Ising model in a transverse field, with dipolar interactions. Quantum annealing has enabled us to explore the quantum and classical phase transitions between the paramagnetic and ferromagnetic phases, at thermodynamical equilibrium. The phase diagram and critical exponents that we obtain agree with expectations for the mean-field universality class.     

Epitaxy surface effect on the first-order phase transition properties in a ferroelectric thin film

By modifying the interchange interactions and the transverse fields on the epitaxy surface layer,this paper studies the phase transition properties of an n-layer ferroelectric thin film by the Fermi-type Green’s function technique based on the transverse Ising model with a four-spin interaction.The special attention is given to the effect of the epitaxy surface layer on the first-order phase transition properties in the parameter space constructed by the ratios of the bulk transverse field and the bulk four-spin interaction to the bulk two-spin interaction with the framework of the higher-order decoupling approximation to the Fermi-type Green’s function.The results show that the first-order phase transition properties will be changed significantly due to the modification of interchange interaction and transverse field parameters on the epitaxy surface layer.The dependence of the first-order phase transition properties on the thickness of ferroelectric thin films is also discussed.