arXiv subjects

Davide Pini

Publications and source records attributed to Davide Pini.

14 recordsLinked to original sources

arXiv2021

Phase diagram of SALR fluids on spherical surfaces

We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous works in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find several inhomogeneous patterns that can be separated into three broad classes: cluster crystals, stripes, and bubble crystals, each containing topological defects. Interestingly, while the periodicity of inhomogeneous phases at large densities is mainly determined by the position of the negative minimum of the potential expansion, the finite size of the system induces a richer behavior at smaller densities.

cond-mat.soft↗

arXiv2021

Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid

Repulsive soft-core atomic systems may undergo clustering if their density is high enough that core overlap is unavoidable. In one-dimensional quantum systems, it has been shown that this instability triggers a transition from a Luttinger liquid to various cluster Luttinger liquids. Here, we focus on the Luttinger liquid regime and theoretically study the evolution of key observables related to density fluctuations, that manifest a striking dependence on density. We tune the interaction so that the low-density regime corresponds to a Tonks-Girardeau gas, and show that as the density is increased the system departs more and more from Tonks-Girardeau behavior, displaying a much larger compressibility as well as rotonic excitations that finally drive the clustering transition. We compare various theoretical approaches, which are accurate in different regimes. Using quantum Monte Carlo methods and analytic continuation as a benchmark, we investigate the regime of validity of the mean-field Bogoliubov and the real-time multiconfiguration time-dependent Hartree-Fock approaches. Part of the behavior that we describe should be observable in ultracold Rydberg-dressed gases, provided that system losses are prevented.

cond-mat.quant-gas↗

arXiv2020

Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose inter-particle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a non-magnetic fluid.

cond-mat.soft↗

arXiv2020

On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model

We provide rigorous evidence that the ordered ground state configurations of a system of parallel oriented, ellipsoidal particles, interacting via a Gaussian interaction (termed in literature as Gaussian core nematics) {\it must} be infinitely degenerate: we have demonstrated that these configurations originate from the related ground state configuration of the corresponding symmetric Gaussian core system via a suitable stretching operation of this lattice in combination with an arbitrary rotation. These findings explain related observations in former investigations, which then remained unexplained. Our conclusions have far reaching consequences for the search of ground state configurations of other nematic particles.

cond-mat.soft↗

arXiv2018

Formation of cluster crystals in an ultra-soft potential model on a spherical surface

We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to clustering: we generalize the criterion devised in C.N. Likos et al., Phys. Rev. E, 2001, 63, 031206 to spherical systems in order to distinguish between cluster forming systems and fluids which display reentrant melting. We use both DFT and Monte Carlo simulations to characterize the behavior of the system, and obtain semi-quantitative agreement between the two. Furthermore, we study the effect of topological frustration on the system due to the sphere curvature by comparing the properties of disclinations, i.e., clusters with fewer than six neighbors, and non-defective clusters. Disclinations are shown to be less stable, contain fewer particles, and be closer to their neighbors than other lattice points: these properties are explained on the basis of geometric and energetic considerations.

cond-mat.soft↗

arXiv2018

Static density response of one-dimensional soft bosons across the clustering transition

One-dimensional bosons interacting via a soft-shoulder potential are investigated at zero temperature. The flatness of the potential at short distances introduces a typical length, such that, at relatively high densities and sufficiently strong interactions, clusters are formed, even in the presence of a completely repulsive potential. We evaluate the static density response function of this system across the transition from the liquid to the cluster liquid phases. Such quantity reveals the density modulations induced by a weak periodic external potential, and is maximal at the clustering wavevector. It is known that this response function is proportional to the static structure factor in the classical regime at high temperature, while for this zero-temperature quantum systems, we extract it from the dynamical structure factor evaluated with quantum Monte Carlo methods.

cond-mat.quant-gas↗

arXiv2017

Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly-interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a composite harmonic chain. Luttinger theory has to be adapted by changing the reference lattice density field. In both the liquid and cluster liquid phases, we find convincing evidence of a secondary mode, which becomes gapless only at the transition. In that region, we also measure the central charge and observe its increase towards c = 3/2, as recently evaluated in a related extended Bose-Hubbard model, and we note a fast reduction of the Luttinger parameter. For 2-particle clusters, we then interpret such observations in terms of the compresence of a Luttinger liquid and a critical transverse Ising model, related to the instability of the reference lattice density field towards coalescence of sites, typical of potentials which are flat at short distances. Even in the absence of a true lattice, we are able to evaluate the spatial correlation function of a suitable pseudo-spin operator, which manifests ferromagnetic order in the cluster liquid phase, exponential decay in the liquid phase, and algebraic order at criticality.

cond-mat.quant-gas↗

arXiv2014

A density-functional theory investigation of cluster formation in an effective-potential model of dendrimers

We consider a system of particles interacting via a purely repulsive, soft-core potential recently introduced to model effective pair interactions between dendrimers, which is expected to lead to the formation of crystals with multiple occupancy of the lattice sites. The phase diagram is investigated by density-functional theory (DFT) without making any a priori assumption on the functional form of the density profile or on the type of crystal lattice. As the average density $ρ$ is increased, the system displays first a transition from a fluid to a bcc phase, and subsequently to hcp and fcc phases. In the inhomogeneous region, the behavior is that found in previous investigations of this class of cluster-forming potentials. Specifically, the particles arrange into clusters strongly localized at the lattice sites, and the lattice constant depends very weakly on $ρ$, leading to an occupancy number of the sites which is a nearly linear function of $ρ$. These results are compared to those predicted by the more widespread approach, in which the DFT minimization is carried out by representing the density profile by a given functional form depending on few variational parameters. We find that for the model potential studied here, the latter approach recovers most of the predictions of the unconstrained minimization.

cond-mat.soft↗

arXiv2011

An investigation of the SCOZA for narrow square-well potentials and in the sticky limit

We present a study of the self consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width delta. The main purpose of this investigation is to elucidate whether in the limit delta --> 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B2(Tc), and whether this theory can lead to an improvement of the approximate Percus-Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)]. For SW of non vanishing delta, the difficulties due to the influence of the boundary condition at high density already encountered in an earlier investigation [E. Schoell-Paschinger, A. L. Benavides, and R. Castaneda-Priego, J. Chem. Phys. 123, 234513 (2005)] prevented us from obtaining reliable results for delta < 0.1. In the sticky limit this difficulty can be circumvented, but then the SCOZA fails to predict a liquid-vapor transition. The picture that emerges from this study is that for delta --> 0, the SCOZA does not fulfill the expected prediction of a constant B2(Tc) [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], and that for thermodynamic consistency to be usefully exploited in this regime, one should probably go beyond the Ornstein-Zernike ansatz.

cond-mat.soft↗

arXiv2010

Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory

Coexistence properties of the hard-core attractive Yukawa potential with inverse-range parameter kappa=9, 10, 12 and 15 are calculated by applying canonical Monte Carlo simulation. As previously shown for longer ranges, we show that also for the ranges considered here the coexistence curves scaled by the critical density and temperature obey the law of corresponding states, and that a linear relationship between the critical density and the reciprocal of the critical temperature holds. The simulation results are compared with the predictions of the self-consistent Ornstein-Zernike approximation, and a good agreement is found for both the critical points and the coexistence curves, although some slight discrepancies are present.

cond-mat.soft↗

arXiv2009

The smooth cut-off Hierarchical Reference Theory of fluids

We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation. A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT. Then, the theory is applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self consistent Ornstein-Zernike approximation is discussed. The asymptotic properties, close to the critical point are investigated and compared to the renormalization group results both above and below the critical temperature. The HRT free energy is always a convex function of the density, leading to flat isotherms in the two-phase region with a finite compressibility at coexistence. This makes HRT the sole liquid-state theory able to obtain directly fluid-fluid phase equilibrium without resorting to the Maxwell construction. The way the mean field free energy is modified due to the inclusion of density fluctuations suggests how to identify the spinodal curve. Thermodynamic properties and correlation functions of the HCYF are investigated for three values of the inverse Yukawa range: z=1.8, z=4 and z=7 where Monte Carlo simulations are available. The stability of the liquid-vapor critical point with respect to freezing is also studied.

cond-mat.soft↗

arXiv2008

Liquid-vapor transition from a microscopic theory: Beyond the Maxwell construction

A smooth cut-off formulation of the Hierarchical Reference Theory (HRT) is developed and applied to a Yukawa fluid. The HRT equations are derived and numerically solved leading to: the expected renormalization group structure in the critical region, non classical critical exponents and scaling laws, a convex free energy in the whole phase diagram (including the two-phase region), finite compressibility at coexistence, together with a fully satisfactory comparison with available numerical simulations. This theory, which also guarantees the correct short range behavior of two body correlations, represents a major improvement over the existing liquid state theories.

cond-mat.stat-mech↗

arXiv2007

Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory

The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.

cond-mat.stat-mech↗

arXiv2001

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions. Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

cond-mat.soft↗