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ABSTRACT: The Hierarchical Reference Theory (HRT) of fluids is a general framework for
the description of phase transitions in microscopic models of classical and
quantum statistical physics. The foundations of HRT are briefly reviewed in a
self-consistent formulation which includes both the original sharp cut-off
procedure and the smooth cut-off implementation, which has been recently
investigated. The critical properties of HRT are summarized, together with the
behavior of the theory at first order phase transitions. However, the emphasis
of this presentation is on the close relationship between HRT and non
perturbative renormalization group methods, as well as on recent
generalizations of HRT to microscopic models of interest in soft matter and
quantum many body physics.
02/2012;
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ABSTRACT: 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.
12/2010;
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ABSTRACT: 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.
02/2009;
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ABSTRACT: We study the rheological properties of colloidal microphases in two dimensions simulating a model of colloidal particles with competing interactions. Due to the competition between short-range attraction and long-range repulsion, as a function of the density the model exhibits a variety of microphases such as clusters, stripes, or crystals with bubbles. We prepare the system in a confined microphase employing Monte Carlo simulations and then shear the resulting configurations by applying a drag force profile. We integrate numerically the equation of motion for the particles and analyze the dynamics as a function of the density and the applied strain rate. We measure the stress-strain curves and characterize the yielding of the colloidal microphases. The results depend on the type of microphase. (i) Clusters are easily sheared along layers and the relative motion is assisted by rotations. (ii) Stripes shear easily when they are parallel to the flow and tend to jam when they are perpendicular to it. Under a sufficiently strong shear rate perpendicular stripes orient in the flow direction. (iii) Crystals with bubbles yield by fracturing along the bubbles and eventually forming stripes. We discuss the role of dislocations, emitted by the bubbles, in the yielding process. Finally, we analyze the effect of thermal fluctuations on the rheological properties.
Physical Review E 09/2008; 78(2 Pt 1):021402. · 2.26 Impact Factor
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ABSTRACT: A smooth cutoff 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, nonclassical 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.
Physical Review Letters 04/2008; 100(16):165704. · 7.37 Impact Factor
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ABSTRACT: We study the effects of confinement between two parallel walls on a two dimensional fluid with competing interactions which lead to the formation of particle microdomains at the thermodynamic equilibrium (microphases or microseparation). The possibility to induce structural changes of the morphology of the microdomains is explored, under different confinement conditions and temperatures. In the presence of neutral walls, a switch from stripes of particles to circular clusters (droplets) occurs as the temperature decreases, which does not happen in bulk. While the passage from droplets to stripes, as the density increases, is a well-known phenomenon, the change of the stripes into droplets as an effect of temperature is rather unexpected. Depending on the wall separation and on the wall-fluid interaction parameters, the stripes can switch from parallel to perpendicular to the walls and also a mixed morphology can be stable.
Physical Review E 11/2007; 76(4 Pt 1):040402. · 2.26 Impact Factor
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ABSTRACT: 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.
Physical Review E 10/2007; 76(3 Pt 1):031113. · 2.26 Impact Factor
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ABSTRACT: We analyze a recent experiment on a Tonks-Girardeau gas of $^{87}$Rb atoms (T. Kinoshita, T. Wenger, and D.S. Weiss, Science {\bf 305}, 1125 (2004)). We find that the experimental data are compatible with the one-dimensional theory of Lieb, Seiringer and Yngvason (Phys. Rev. Lett. {\bf 91}, 150401 (2003)) but are better described by a theory that takes into account variations in the transverse width of the atomic cloud. By using this theory we investigate also the free axial expansion of the $^{87}$Rb gas in different regimes: Tonks-Girardeau gas, one-dimensional Bose-Einstein condensate and three-dimensional Bose-Einstein condensate. Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. A
07/2005;
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ABSTRACT: 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 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 non-classical 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 non universal 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. Comment: To be published in Phy. Rev. E
09/2004;
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ABSTRACT: We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density when non locality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number $N$ of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system as the strength of the effective interaction increases with $N$. Comment: 11 pages, Latex, 2 figures, to be published in Phys. Rev. A
03/1998;
