1,195 research outputs found
Implementation of the Hierarchical Reference Theory for simple one-component fluids
Combining renormalization group theoretical ideas with the integral equation
approach to fluid structure and thermodynamics, the Hierarchical Reference
Theory is known to be successful even in the vicinity of the critical point and
for sub-critical temperatures. We here present a software package independent
of earlier programs for the application of this theory to simple fluids
composed of particles interacting via spherically symmetrical pair potentials,
restricting ourselves to hard sphere reference systems. Using the hard-core
Yukawa potential with z=1.8/sigma for illustration, we discuss our
implementation and the results it yields, paying special attention to the core
condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio
Phase diagram of symmetric binary mixtures at equimolar and non-equimolar 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 (HRT). 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 < delta < 1,
we find first a regime where the phase diagram at equal species concentration
displays a tricritical point, then one where both a tricritical and a
liquid-vapor critical point are present. We did not find any clear evidence of
the critical endpoint topology predicted by mean-field theory as delta
approaches 1, at least up to delta=0.8, which is the largest value of delta
investigated here. Particular attention was paid to the description of the
critical-plus-tricritical point regime in the whole density-concentration
plane. In this situation, the phase diagram shows, in a certain temperature
interval, a coexistence region that encloses an island of homogeneous,
one-phase fluid.Comment: 27 pages + 20 figure
Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
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.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic
Phase transitions in simple and not so simple binary fluids
Compared to pure fluids, binary mixtures display a very diverse phase
behavior, which depends sensitively on the parameters of the microscopic
potential. Here we investigate the phase diagrams of simple model mixtures by
use of a microscopic implementation of the renormalization group technique.
First, we consider a symmetric mixture with attractive interactions, possibly
relevant for describing fluids of molecules with internal degrees of freedom.
Despite the simplicity of the model, slightly tuning the strength of the
interactions between unlike species drastically changes the topology of the
phase boundary, forcing or inhibiting demixing, and brings about several
interesting features such as double critical points, tricritical points, and
coexistence domains enclosing `islands' of homogeneous, mixed fluid.
Homogeneous phase separation in mixtures can be driven also by purely repulsive
interactions. As an example, we consider a model of soft particles which has
been adopted to describe binary polymer solutions. This is shown to display
demixing (fluid-fluid) transition at sufficiently high density. The nature and
the physical properties of the corresponding phase transition are investigated.Comment: 6 pages + 3 figures, presented at the 5th EPS Liquid Matter
Conference, Konstanz, 14-18 September 200
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.Comment: 8 pages, 4 figure
Condensate Fraction of a Fermi Gas in the BCS-BEC Crossover
We investigate the Bose-Einstein condensation of Fermionic pairs in a uniform
two-component Fermi gas obtaining an explicit formula for the condensate
density as a function of the chemical potential and the energy gap. We analyze
the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer
(BCS) state of weakly-interacting Cooper pairs to the Bose-Einstein Condensate
(BEC) of molecular dimers. By using the local density approximation we study
confined Fermi vapors of alkali-metal atoms for which there is experimental
evidence of condensation also on the BCS side of the Feshbach resonance. Our
theoretical results are in agreement with these experimental data and give the
behavior of the condensate on both sides of the Feshbach resonance at zero
temperature.Comment: 5 pages, 2 figure
Magneto-elastic effects and magnetization plateaus in two dimensional systems
We show the importance of both strong frustration and spin-lattice coupling
for the stabilization of magnetization plateaus in translationally invariant
two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model
coupled to adiabatic phonons under an external magnetic field. At zero
magnetization, simple structures with two or at most four spins per unit cell
are stabilized, forming dimers or plaquettes, respectively. A much
richer scenario is found in the case of magnetization , where larger
unit cells are formed with non-trivial spin textures and an analogy with the
corresponding classical Ising model is detectable. Specific predictions on
lattice distortions and local spin values can be directly measured by X-rays
and Nuclear Magnetic Resonance experiments.Comment: 4 pages and 4 figure
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