Phase diagram of lithium-doped copper oxide, Cu1−xLixO

Heat capacities of lithium-doped samples of CuO have been measured below room temperature by adiabatic calorimetry. The antiferromagnetic ordering transition to incommensurately modulated state was detected as a step in the heat capacity. Its concentration dependence was compatible with existing reports based on Li-NMR. The incommensurate-commensurate transition of lithium-doped copper oxide was clearly detected for the first time. The magnetic phase diagram of Cu_1−xLi_xO was thus constructed. The suppression of both transition temperatures by the Li doping is nearly twice as strong as that expected from mean-field and percolation theories.     

Infinite Range Interaction Model of a Structural Glass

In this paper a simple mean-field model for the liquid-glass phase transition is proposed. This is the low density D-dimensional system of N particles interacting via infinite-range oscillating potential. In the framework of the replica approach it is shown that such a system exhibits the phase transition between the high-temperature liquid phase and the low-temperature glass phase. This phase transition is described in terms of the standard one-step replica symmetry breaking scheme.     

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.     

Mean-field approach to Z(N) gauge systems with generalized action

The phase diagram of Z(N) lattice gauge theories with generalized action is examined in the mean-field approach. The phase diagram is well reproduced, with the exception of the Coulomb phase, which is absent. A previously identified mechanism that dynamically generates the Coulomb phase from quantum fluctuations is shown to give agreement with Monte Carlo data in four dimensions.     

Recognition ability of the fully connected Hopfield neural network under a persistent stimulus field

We investigate the pattern recognition ability of the fully connected Hopfield model of a neural network under the influence of a persistent stimulus field. The model considers a biased training with a stronger contribution to the synaptic connections coming from a particular stimulated pattern. Within a mean-field approach, we computed the recognition order parameter and the full phase diagram as a function of the stimulus field strength h, the network charge α and a thermal-like noise T. The stimulus field improves the network capacity in recognizing the stimulated pattern while weakening the first-order character of the transition to the non-recognition phase. We further present simulation results for the zero temperature case. A finite-size scaling analysis provides estimates of the transition point which are very close to the mean-field prediction.     

Interpretation of the specific heat at the Jahn-Teller phase transition in DyVO4 using a “compressible” Ising model

The specific heat at the Jahn-Teller phase transition in DyVO₄ is too sharply peaked to be explained by simple mean-field theory, but is very well described by using a mean-field model in which the effective interaction increases upon ordering according to J′=J₀′(1+ζ〈σ^z〉²) where ζ is an adjustable parameter.     

Quantum phase transitions in the sub-Ohmic spin-boson model: failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive mapping fails for the sub-Ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional, variantomega(s). Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.     

Noisy Hegselmann-Krause Systems: Phase Transition and the 2<Emphasis Type="Italic">R</Emphasis>-Conjecture

The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. We introduce an order parameter to track the phase transition and resolve the corresponding phase diagram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis confirms previous simulations and predicts properties of the noisy HK model in higher dimension.     

Mean-field theory of the three-state chiral clock model

The phase diagram of the three-state chiral clock model, which is known to exhibit commensurate and incommensurate ordered modulated structures, is investigated in the mean-field approximation. First a numerical analysis of the mean-field equations is presented. It is based in the main on the observation that these equations define a non-linear mapping in a four dimensional space. This method of analyzing the mean-field theory proves particularly useful in the determination of the pinning transition of the incommensurate structures. Next the phase diagram is investigated analytically by means of a Landau expansion modified such as to include domain walls. It is found that in the vicinity of the order-disorder transition most features of the phase diagram can be explained quantitatively by this expansion. Finally we present a systematic lowtemperature expansion of the mean-field theory, showing that the low-temperature phase diagram obtained in the mean-field approximation is different from that of the full model.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

The two-dimensional extended Holstein-Hubbard model is investigated in the strong correlation regime to study the nature of self-trapping transition and the polaron phase diagram in the absence of superconductivity. Using a series of canonical transformations followed by zero-phonon averaging the extended Holstein-Hubbard model is converted into an effective extended Hubbard model which is subsequently transformed into an effective t-J model in the strong correlation limit. This effective t-J model is finally solved using the mean-field Hartree-Fock approximation to show that the self-trapping transition is continuous in the anti-adiabatic limit while it is discontinuous in the adiabatic limit. The phase diagrams for the localization-delocalization transition, namely the phase line and the phase surface separating the small polaron and large polaron states are also shown.     

Mean-Field Analysis of the q-Voter Model on Networks

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.     

Finite temperature neutral-ionic transition and lattice dimerization in charge-transfer complexes: QMC study

We numerically investigate the neutral-ionic (NI) phase transition on the basis of the ionic extended Hubbard model with electron-lattice coupling as well as inter-chain Coulomb interaction. Finite-temperature (T) phase transitions are examined by a quantum Monte Carlo method, within adiabatic approximation for the lattice displacement together with inter-chain mean-field treatment. The NI transition either with or without the electron-lattice coupling is of first-order at low-T and transforms into a cross-over regime with increasing T. We confirm there exist two phases in the ionic region: with and without lattice dimerization, as suggested in recent experiments. The former is ferroelectric, which is rooted in the Coulomb interactions and a spin-Peierls mechanism.     

Competition between crystalline electric field singlet and itinerant states of f electrons

A new kind of phase transition is proposed for lattice fermion systems with simplified f ² configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contrast with the Mott transition in the Hubbard model. For comparison, corresponding states are discussed for the twoimpurity Kondo system with f ¹ configuration at each site.     

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.     

An effective-field study of Ising metamagnet in an external field

The phase diagrams and magnetization curves of a two-sublattice Ising metamagnet at finite temperature with longitudinal crystal field H are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented, since a method to calculate the Gibbs free energy numerically at finite temperature within EFT is found in this work. The results show that there is no fourth-order critical point or reentrant phenomenon in the phase diagrams given by using EFT as found by using mean-field theory (MFT).     

Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U _c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U _m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U _c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.     

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite-temperature symmetry-restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the (3 + 1)-dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean-field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, m_H = 37 GeV, considered in the present investigation, we find a discontinuous symmetry-restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first-order phase transition as compared to the mean-field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first-order transition could result only from non-perturbative effects related to the gauge degrees of freedom.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.