Semiclassical shell-structure moment of inertia for equilibrium rotation of a simple Fermi system

Semiclassical shell-structure components of the collectivemoment of inertia are derived within the mean-field cranking model in the adiabatic approximation in terms of the free-energy shell corrections through those of a rigid body for the statistically equilibriumrotation of a Fermi system at finite temperature by using the nonperturbative extended Gutzwiller periodic-orbit theory. Their analytical structure in terms of the equatorial and 3-dimensional periodic orbits for the axially symmetric harmonic oscillator potential is in perfect agreement with the quantum results for different critical bifurcation deformations and different temperatures.     

Density fluctuations in the presence of spinodal instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.     

Renormalization group analysis of the random first-order transition

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in the mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

Ground state of a spin system with two- and four-spin exchange interactions on the triangular lattice

We study a spin system with both two- and four-spin exchange interactions on the triangular lattice as a possible model for the nuclear magnetism of solid ³He layers adsorbed on grafoil. The ground state is analyzed by the use of the mean-field approximation. It is shown that the four-sublattice state is favored by introduction of the fourspin exchange interaction. A possible phase transition at a finite temperature into a phase with the scalar chirality is predicted. Application of a magnetic field is shown to cause a variety of phase transitions.     

Ising models with two- and three-spin interactions: Mean field equation of state

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J₂ > 0.75J₃ only the latter transition remains.     

Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

Quantum phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Going to 10 TPa: The Calculated Hugoniots for Cu,Ta, and Mo

The Hugoniot equations of state for shock compressed Cu, Ta, and Mo are calculated at pressures up to 4 TPa and then up to 10 TPa are obtained by extrapolation. The calculations are parameter-free in that the cold part of the Helmholtz free-energy is calculated using the first-principles full-potential linearized augmented plane wave method within the generalized gradient approximation, the thermal contribution to the Helmholtz free-energy due to the lattice oscillations is calculated using the recently developed classical mean-field potential approach, and that due to the thermal electrons is calculated using the one-dimensional numerical integration. The calculated results agree with the existing experimental values very well.     

Coherent potential approximation study of the Mott transition in optical lattice system with site-dependent interactions

We study the Mott transition in the half-filled Hubbard model with spatially alternating interactions by means of the coherent potential approximation. The phase boundary between metallic and insulating phases at zero temperature is derived and the nature of the Mott states is also considered. Our results are in good agreement with the ones recently obtained by the two-site dynamical mean-field theory.     

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order–disorder phase transformations driven by a bulk free-energy difference. The solid-on-solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.     

Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent ν for the localization length to be 1.45 ± 0.09 with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.     

Mean-field approximation for the potts model of a diluted magnet in the external field

The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.     

Lattice-gas model of multiple layer adsorption

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.     

The extended quark sigma model at finite temperature and baryonic chemical potential

An extended quark sigma model which includes higher-order mesonic interactions is studied at the finite baryonic chemical potential u _B and temperature T. The field equations have been solved in the mean-field approximation by using the modified iteration method at finite baryonic chemical potential u _B and temperature T. The Goldstone theorem is satisfied below a critical temperature in the chiral limit for u _B = 0. As expected from general universality, the chiral phase transition is second-order. By including the higher-order mesonic interactions, the critical temperature is reduced compared to that found in recent works and is in good agreement with lattice QCD results. The nucleon mass is examined in the (u _B , T) plane, showing a strong dependence on u _B and T. We find that an increase in both the baryonic chemical potential u _B and the temperature T leads to an increase in the values of the nucleon mass. This is evidence for the quark-gluon deconfinement phase transition at higher values of temperature.     

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.     

Generic absorbing transition in coevolution dynamics

We study a coevolution voter model on a complex network. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value [see text for formula] that only depends on the average degree micro of the network. In finite-size systems, the active and frozen phases correspond to a connected and a fragmented network, respectively. The transition can be seen as the sudden change in the trajectory of an equivalent random walk at the critical point, resulting in an approach to the final frozen state whose time scale diverges as tau approximately |p(c) - p|(-)} near p(c).     

Effects of disorder on ferromagnetism in diluted magnetic semiconductors

We present results of a numerical mean-field treatment of interacting spins and carriers in doped diluted magnetic semiconductors, which takes into account the positional disorder present in these alloy systems. Within our mean-field approximation, disorder enhances the ferromagnetic transition temperature for metallic densities not too far from the metal-insulator transition. Concurrently, the ferromagnetic phase is found to have very unusual temperature dependence of the magnetization as well as specific heat as a result of disorder. Unusual spin and charge transport is implied.     

Quark matter properties and fluctuations of conserved charges in (2+1)-flavored quark model

In this study, the susceptibilities of conserved charges, baryon number, charge number, and strangeness number at zero and low values of chemical potential are presented. Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson (PQM) model and the Polyakov loop extended chiral quark mean-field (PCQMF) model. Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential, as well as the vector interactions. The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed. A comparative analysis of the two models was completed. Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point (CEP). Susceptibilities of conserved quantities were calculated by using the Taylor series method. Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics (QCD) critical-point.