Nonequilibrium quantum criticality in open electronic systems

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant-electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.     

On the equivalence between magnetic-field-induced phase transitions in the integer quantum Hall effect

Magnetic-field-induced phase transitions in the two-dimensional electron system in a AlGaAs/InGaAs/GaAs heterostructure are studied. Two kinds of magnetic-field-induced phase transitions, plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions, are observed in the integer quantum Hall effect regime at high magnetic fields. In the P-P transition, both the semicircle law and the universality of critical conductivities are broken and we do not observe the universal scaling. However, the P-P transition can still be mapped to the I-QH transition by the Landau-level addition transformation, and as the temperature decreases the critical points of these two transitions appear at the same temperature. Our observations indicate that the equivalence between P-P and I-QH transitions can be found by the suitable analysis even when some expected universal properties are invalid.     

Phase transitions in barium–strontium titanate films on MgO substrates with various orientations

A comparative study of the lattice dynamic upon phase transitions in a polycrystalline Ba_0.8Sr_0.2TiO₃ (BST) film on a Pt substrate and in epitaxial BST films grown on various sections of an MgO substrate has been performed by Raman spectroscopy. It has been found that different sequences of phase transitions take place in these films. The BST/Pt films demonstrate the same sequence of phase transitions that is observed in the bulk ceramics. The hardening of a soft mode in BST/(001)MgO and BST/Pt films shows that the transition from the tetragonal ferroelectric phase to the paraelectric phase has features of the displacement-type phase transition and also the order–disorder phase transition. When approaching the ferroelectric transition temperature, the soft mode in the BST/(111)MgO film is softened, following the Cockran law, which indicates the displacement-type phase transition.     

Group-theoretical description of domain and phase boundaries in crystalline solids

The theory is reviewed of domains and domain boundaries arising in phase transitions accompanied by symmetry breaking. Conclusions concerning the number, the crystallographic type and the spatial orientation of coherent interfaces between crystals of the same structure (domain boundaries) and between different structures of the same material (interphase boundaries) are presented in terms of the space group theory and of the Landau theory of phase transitions. The application of the two-dimensional space groups and the diperiodic groups in three dimensions to the discussed objects is described. The conditions for the coexistence of domains and phases without macroscopic stress are given. An example of the group-theoretical analysis of domain structure is given for a real material: NaO₂.     

First measurements by the EDXD-PT technique of the effect of the melting time on polymer crystallization kinetics

A nonconventional energy-depressive X-ray diffraction method applied to phase transitions (EDXD-PT) was used to measure polymer crystallization rates. It enables one to follow the kinetics of phase transitions by a direct comparison of diffraction patterns collected during the process and suitably normalized with respect to X-ray absorption spectra taken with the same time scan. With this technique, the memory that a polymer retains of its thermal history is investigated by correlating the crystallization rates to the residence time in the melt.     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross－Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.     

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.     

Correlating radii and electric monopole transitions of atomic nuclei

A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from 58Ce to 74W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom (g boson) on the correlation between radii and E0 transitions thus established is discussed.     

Phase Transition Induced by Small Molecules in Confined Copolymer Films

We investigate the phase transition induced by small molecules in confined copolymer films by using density functional theory. It is found that the addition of small molecules can effectively promote the phase separation of copolymers. In a symmetric diblock copolymer film, the affinity and concentration of small molecules play an important role in the structure transitions. The disordered-lamellar transitions, larnellar-lamellar transitions and the re-entrant transitions of the same structures are observed. Our results have potential applications in the fabrication of new functional materials.     

Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions

Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.     

Fractional phase transitions of RN-AdS black holes at their Davies points

In this study, we investigate the phase transitions of the RN-AdS black hole at its Davies points according to the generalized Ehrenfest classification of phase transition established based on fractional derivatives. Notably, Davies points label the positions at which the heat capacity diverges. According to the usual Ehrenfest classification, second-order phase transitions occur at these points. For the RN-AdS black hole, the Davies points can be classified into two types. The first type corresponds to extreme values of the temperature, and the second type corresponds to the infection point (namely the critical point) of temperature. Employing the generalized Ehrenfest classification, we determine that the orders of phase transition at the two types of Davies points are different, that is, we note an order of 3/2 for the first type and 4/3 for the second type. Thus, this finer-grained classification can discriminate between phase transitions that are expected to lie in the same category, providing new insights leading toward a better understanding of black hole thermodynamics.     

Polarization interaction and phase transitions in crystals with two interacting subsystems

The influence of the polarization interactions on the state and phase transitions in magnetic-ordered and dielectric crystals with two interacting order parameters has been investigated. Consideration is given to the case when the interaction in one of the subsystems is considerably weaker than that in the other subsystem. It is demonstrated that the polarization interactions in the weak subsystem can substantially affect the state and the character of phase transitions in the strong subsystem. These interactions can bring about the disordering (formation of the random-field state or the state of spin glass) in the critical region near the second-order phase transition in the main subsystem and also the smearing of the phase transition. At the same time, the polarization interactions can give rise to the ordered and disordered states in the weak subsystem.     

Comparative study of liquid-crystalline ordering in a monomer,linear polymer,and graft copolymer by the photon transmission technique

The photon transmission technique was used to study the phase transitions of a liquid crystalline acrylate monomer, 6-(4-cyanobiphenyl-4′oxy)hexyl acrylate (LC6), its homopolymer (PLC6) and its graft copolymer (GLC6) with polytetrahydrofuran grafts. The phase transitions were also confirmed by DSC and polarizing microscopy. We observed the phase transition sequence isotropic–nematic–smectic A–smectic C in the LC6 monomer. In PLC6 and GLC6 polymers, the nematic and smectic A phases appear dominant. The apparent nematic–smectic A transition is of first order in PLC6 and of second order in GLC6, with the transition temperature remaining the same. The effects of quenched random constraints introduced in GLC6 are consistent with the theory of quenched random interactions. The critical exponents were also evaluated.     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.     

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.     

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.     

Absence of second-order phase transitions in the Dobrushin uniqueness region

The Dobrushin uniqueness theorem assures that in a very large class of high-temperature classical statistical mechanical lattice models with short or long range, many-body interactions, and arbitrary compact spin space there are no first-order phase transitions. It will be shown that for the same class of interactions there are also no second-order phase transitions.Research partially supported by the National Science Foundation under Grant MCS 78-00688.     

The Strength of First and Second Order Phase Transitions from Partition Function Zeroes

We present a numerical technique employing the density of partition function zeroes (i) to distinguish between phase transitions of first and higher order, (ii) to examine the crossover between such phase transitions and (iii) to measure the strength of first and second order phase transitions in the form of latent heat and critical exponents. These techniques are demonstrated in applications to a number of models for which zeroes are available.     

Instability transitions and ensemble equivalence in diffusive flow

We investigate the critical behavior of one-dimensional (1D) stochastic flow with competing nonlocal and local hopping events, in context of the totally asymmetric simple exclusion process (TASEP) with a defect site in a 1D closed chain. The defect site can effectively generate various boundary conditions, controlling the total number of particles in the system. Both open and periodic-like setups exhibit dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. In the stationary populated phase, strong clustering promoted by nonlocal skids drives such transitions and determines their scaling properties. By static and dynamic simulations, we locate such transition points, and discuss their nature and scaling properties. In the open TASEP variant, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current, while it is first order in the regime where the bulk controls the current. Since it is well known that such transitions are absent in the periodic TASEP variant, we compare our results in the open setup with those in the periodic-like setup, and discuss the issue of the ensemble equivalence. Finally, the same discussion is extended to the symmetric cases.