2,834 research outputs found
Statistical mechanics and dynamics of solvable models with long-range interactions
The two-body potential of systems with long-range interactions decays at
large distances as , with , where is the
space dimension. Examples are: gravitational systems, two-dimensional
hydrodynamics, two-dimensional elasticity, charged and dipolar systems.
Although such systems can be made extensive, they are intrinsically non
additive. Moreover, the space of accessible macroscopic thermodynamic
parameters might be non convex. The violation of these two basic properties is
at the origin of ensemble inequivalence, which implies that specific heat can
be negative in the microcanonical ensemble and temperature jumps can appear at
microcanonical first order phase transitions. The lack of convexity implies
that ergodicity may be generically broken. We present here a comprehensive
review of the recent advances on the statistical mechanics and
out-of-equilibrium dynamics of systems with long-range interactions. The core
of the review consists in the detailed presentation of the concept of ensemble
inequivalence, as exemplified by the exact solution, in the microcanonical and
canonical ensembles, of mean-field type models. Relaxation towards
thermodynamic equilibrium can be extremely slow and quasi-stationary states may
be present. The understanding of such unusual relaxation process is obtained by
the introduction of an appropriate kinetic theory based on the Vlasov equation.Comment: 118 pages, review paper, added references, slight change of conten
Ternary and quaternary oxides of Bi, Sr, and Cu
Before the discovery of superconductivity in an oxide of Bi, Sr, and Cu, the system Bi-Sr-Cu-O had not been studied, although several solid phases had been identified in the two-component regions of the ternary system Bi2O3-SrO-CuO. The oxides Sr2CuO3, SrCu2O2, SrCuO2, and Bi2CuO4 were then well known and characterized, and the phase diagram of the binary system Bi2O3 -SrO had been established in the temperature range 620 to 1000 C. Besides nine solutions of compositions Bi(2-2x) Sr(x) O(3-2x) and different symmetries, this diagram includes three definite compounds of stoichiometries Bi(2)SrO4, Bi2Sr2O5, and Bi2Sr3O6 (x = 0.50, 0.67 and 0.75 respectively), only the second of which with known unit-cell of orthorhombic symmetry, dimensions (A) a = 14.293(2), b = 7.651(2), c = 6.172(1), and z = 4. The first superconducting oxide in the system Bi-Sr-Cu-O was initially formulated as Bi2Sr2Cu2O(7+x), with an orthorhombic unit-cell of parameters (A) a = 5.32, b = 26.6, c = 48.8. In a preliminary study the same oxide was formulated with half the copper content, Bi(2)Sr(2)CuO(6+x), and indexed its reflections assuming an orthorhombic unit-cell of dimensions (A) a = 5.390(2), b = 26.973(8), c = 24.69(4). Subsequent studies by diffraction techniques have confirmed the composition 2:2:1. A new family of oxygen-deficient perovskites, was characterized, after identifying by x ray diffraction the phases present in the products of thermal treatments of about 150 mixtures of analytical grade Bi2O3, Sr(OH)2-8H2O and CuO at different molar ratios. X ray diffraction data are presented for some other oxides of Bi and Sr, as well as for various quaternary oxides, among them an oxide of Bi, Sr, and Cu
Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
Classical spin systems with nonadditive long-range interactions are studied
in the microcanonical ensemble. It is expected that the entropy of such a
system is identical to that of the corresponding mean-field model, which is
called "exactness of the mean-field theory". It is found out that this
expectation is not necessarily true if the microcanonical ensemble is not
equivalent to the canonical ensemble in the mean-field model. Moreover,
necessary and sufficient conditions for exactness of the mean-field theory are
obtained. These conditions are investigated for two concrete models, the
\alpha-Potts model with annealed vacancies and the \alpha-Potts model with
invisible states.Comment: 23 pages, to appear in J. Stat. Phy
Enhancement of magnetic anisotropy barrier in long range interacting spin systems
Magnetic materials are usually characterized by anisotropy energy barriers
which dictate the time scale of the magnetization decay and consequently the
magnetic stability of the sample. Here we present a unified description, which
includes coherent rotation and nucleation, for the magnetization decay in
generic anisotropic spin systems. In particular, we show that, in presence of
long range exchange interaction, the anisotropy energy barrier grows as the
volume of the particle for on site anisotropy, while it grows even faster than
the volume for exchange anisotropy, with an anisotropy energy barrier
proportional to , where is the particle volume, is the range of interaction and is the embedding dimension. These
results shows a relevant enhancement of the anisotropy energy barrier w.r.t.
the short range case, where the anisotropy energy barrier grows as the particle
cross sectional area for large particle size or large particle aspect ratio.Comment: 7 pages, 6 figures. Theory of Magnetic decay in nanosystem. Non
equilibrium statistical mechanics of many body system
1-d gravity in infinite point distributions
The dynamics of infinite, asymptotically uniform, distributions of
self-gravitating particles in one spatial dimension provides a simple toy model
for the analogous three dimensional problem. We focus here on a limitation of
such models as treated so far in the literature: the force, as it has been
specified, is well defined in infinite point distributions only if there is a
centre of symmetry (i.e. the definition requires explicitly the breaking of
statistical translational invariance). The problem arises because naive
background subtraction (due to expansion, or by "Jeans' swindle" for the static
case), applied as in three dimensions, leaves an unregulated contribution to
the force due to surface mass fluctuations. Following a discussion by
Kiessling, we show that the problem may be resolved by defining the force in
infinite point distributions as the limit of an exponentially screened pair
interaction. We show that this prescription gives a well defined (finite) force
acting on particles in a class of perturbed infinite lattices, which are the
point processes relevant to cosmological N-body simulations. For identical
particles the dynamics of the simplest toy model is equivalent to that of an
infinite set of points with inverted harmonic oscillator potentials which
bounce elastically when they collide. We discuss previous results in the
literature, and present new results for the specific case of this simplest
(static) model starting from "shuffled lattice" initial conditions. These show
qualitative properties (notably its "self-similarity") of the evolution very
similar to those in the analogous simulations in three dimensions, which in
turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added
discussion in section IV), matches final version to appear in PR
Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems
We derive a necessary and sufficient condition of linear dynamical stability
for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF)
model. The condition is expressed by an explicit disequality that has to be
satisfied by the stationary state, and it generalizes the known disequality for
homogeneous stationary states. In addition, we derive analogous disequalities
that express necessary and sufficient conditions of formal stability for the
stationary states. Their usefulness, from the point of view of linear dynamical
stability, is that they are simpler, although they provide only sufficient
criteria of linear stability. We show that for homogeneous stationary states
the relations become equal, and therefore linear dynamical stability and formal
stability become equivalent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen
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