Path integral Monte Carlo study of 4He clusters doped with alkali and alkali-earth ions.

Path integral Monte Carlo calculations of (4)He nanodroplets doped with alkali (Na(+), K(+) and Cs(+)) and alkali-earth (Be(+) and Mg(+)) ions are presented. We study the system at T = 1 K and between 14 and 128 (4)He atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized (4)He atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of (4)He atoms in the first shell varies from 12 for Na(+) to 18 for Mg(+) and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na(+) giving a very stable icosahedral order extending up to three shells.

Exact ground state Monte Carlo method for Bosons without importance sampling.

Generally "exact" quantum Monte Carlo computations for the ground state of many bosons make use of importance sampling. The importance sampling is based either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of path integral ground state (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a nonzero overlap with the ground state, which gives rise to a discrete path which is sampled via a Metropolis-like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid (4)He with PIGS by considering as initial wave function a constant, i.e., the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e., there is no importance sampling. For both phases we obtain results converging to those obtained by considering the best available variational wave function (the shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance, a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function, and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature path integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

Dynamical arrest and replica symmetry breaking in attractive colloids.

Within the replica symmetry breaking framework developed by Mézard and Parisi we investigate the occurrence of structural glass transitions in a model of fluid characterized by hard sphere repulsion together with short-range attraction. This model is appropriate for the description of a class of colloidal suspensions. The transition line in the density-temperature plane displays a reentrant behavior, in agreement with mode coupling theory and recent molecular dynamics simulations. Quantitative differences are found, together with the absence of the predicted glass-glass transition at high density. We also perform a systematic study of the pure hard-sphere fluid in order to ascertain the accuracy of the adopted method and the convergence of the numerical procedure.

Critical behavior in colloid-polymer mixtures: theory and simulation.

We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.

Construction of an effective Hamiltonian for a three-dimensional Ising universality class.

The asymptotic and preasymptotic critical behavior in fluids, mixtures, and uniaxial magnets is believed to be described by an effective straight phi(4) scalar field theory with suitable, nonuniversal, coupling constants. The critical parameters as well as the extent of crossovers and corrections to the leading critical behavior in physical systems, crucially depends on the choice of these couplings. Here we propose a new method for deriving the effective scalar field theory appropriate to a microscopic model in this universality class. Use is made of the hierarchical reference theory, which implements the basic ideas of Wilson momentum space renormalization group to microscopic Hamiltonians. The effective low-energy field theory is then analyzed by the minimal subtraction scheme of Schloms and Dohm. We discuss the application of this method to the three-dimensional Ising model and to the liquid-vapor phase transition. We make comparison with high-temperature expansion results and with experimental data for rare gas.

Hierarchical reference theory study of the lattice restricted primitive model.

A three dimensional model of point charges, named lattice restricted primitive model (LRPM), is investigated by using the hierachical reference theory of fluids. This approach, which generalizes the momentum renormalization group technique, is shown to capture the physics of the model and provides a quantitative description of the phase diagram. The comparison with recent numerical simulations and with other theoretical approaches is discussed both for the LRPM and for the Blume-Capel model, which can be seen as a screened version of LRPM. The nonuniversal crossover region close to the tricritical point is also discussed.

Microscopic approach to critical phenomena at interfaces: an application to complete wetting in the Ising model.

We study how the formalism of the hierarchical reference theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid-state theory which implements the basic ideas of the Wilson momentum-shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and nonclassical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the nonuniversal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.

Phase diagram of symmetric binary mixtures at equimolar and nonequimolar concentrations: a systematic investigation.

We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As delta is increased in the interval 0

Star polymers: a study of the structural arrest in the presence of attractive interactions.

Simulations and mode-coupling theory calculations, for a large range of the arm number f and packing fraction eta have shown that the structural arrest and the dynamics of star polymers in a good solvent are extremely rich: the systems show a reentrant melting of the disordered glass nested between two stable fluid phases that strongly resemble the equilibrium phase diagram. Starting from a simple model potential we investigate the effect of the interplay between attractive interactions of different range and ultrasoft core repulsion, on the dynamics and on the occurrence of the ideal glass transition line. In the two cases considered so far, we observed some significant differences with respect to the purely repulsive pair interaction. We also discuss the interplay between equilibrium and nonequilibrium phase behavior. The accuracy of the theoretical tools we utilized in our investigation has been checked by comparing the results with molecular dynamics simulations.

Many-body interaction effects on the low-k structure of liquid Kr.

Neutron diffraction measurements and theoretical calculations of the structure factor S(k) of liquid Kr are extended to small k values (k<4 nm(-1)). The results show that many-body interaction contributions have an increasing effect on S(k) as k-->0, reaching at least 40% of the measured intensity. Both the phase diagram and the low-k structural data of dense Kr turn out to be closely reproduced by the hierarchical reference theory if additional many-body forces are taken into account by an augmented strength of the Axilrod-Teller triple-dipole potential. The experimental density derivative of S(k) is also used for a very sensitive test of the theories and interaction models considered here.

A density-functional theory study of microphase formation in binary Gaussian mixtures.

We use density-functional theory to study the formation of inhomogeneous phases in a binary mixture of particles interacting by repulsive, athermal Gaussian potentials with suitably chosen strengths and ranges. Both the potential parameters and the free-energy functional are the same as those adopted in a previous investigation by other authors (Archer A J, Likos C N and Evans R 2004 J. Phys.: Condens. Matter 16 L297), but here a fully numerical minimization of the functional is performed, without any assumption about the functional form of the density profile. We find lamellar, rod and cluster phases. In the lamellar phase, the two species arrange into intercalating stripes; in the rod and cluster phases, the minority species is localized at the site of a periodic lattice, either triangular (for rods) or body-centred cubic (for clusters), while the other species is distributed non-uniformly in the remaining region, so that it forms a percolating network. The order of the transition from the homogeneous to the inhomogeneous phase and the phase diagram of the mixture are also discussed.

Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He.

Defects are believed to play a fundamental role in the supersolid state of (4)He. We have studied solid (4)He in two dimensions (2D) as a function of the number of vacancies n(v), up to 30, inserted in the initial configuration at ρ=0.0765 Å( - 2), close to the melting density, with the exact zero-temperature shadow path integral ground state method. The crystalline order is found to be stable also in the presence of many vacancies and we observe two completely different regimes. For small n(v), up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n(v), the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. It is no longer possible to recognize vacancies in the equilibrated state because they mainly transform into quantum dislocations and crystalline order is found almost independently of how many vacancies have been inserted in the initial configuration. The one-body density matrix in this latter regime shows a non-decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of the incommensurate versus the commensurate state loses meaning for solid (4)He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in the presence of up to 100 vacancies.