3,777 research outputs found
Asymmetric Fluid Criticality I: Scaling with Pressure Mixing
The thermodynamic behavior of a fluid near a vapor-liquid and, hence,
asymmetric critical point is discussed within a general ``complete'' scaling
theory incorporating pressure mixing in the nonlinear scaling fields as well as
corrections to scaling. This theory allows for a Yang-Yang anomaly in which
\mu_{\sigma}^{\prime\prime}(T), the second temperature derivative of the
chemical potential along the phase boundary, diverges like the specific heat
when T\to T_{\scriptsize c}; it also generates a leading singular term,
|t|^{2\beta}, in the coexistence curve diameter, where t\equiv
(T-T_{\scriptsize c}) /T_{\scriptsize c}. The behavior of various special loci,
such as the critical isochore, the critical isotherm, the k-inflection loci, on
which \chi^{(k)}\equiv \chi(\rho,T)/\rho^{k} (with \chi = \rho^{2}
k_{\scriptsize B}TK_{T}) and C_{V}^{(k)}\equiv C_{V}(\rho,T)/\rho^{k} are
maximal at fixed T, is carefully elucidated. These results are useful for
analyzing simulations and experiments, since particular, nonuniversal values of
k specify loci that approach the critical density most rapidly and reflect the
pressure-mixing coefficient. Concrete illustrations are presented for the
hard-core square-well fluid and for the restricted primitive model electrolyte.
For comparison, a discussion of the classical (or Landau) theory is presented
briefly and various interesting loci are determined explicitly and illustrated
quantitatively for a van der Waals fluid.Comment: 21 pages in two-column format including 8 figure
Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions
Finite-size scaling functions are investigated both for the mean-square
magnetization fluctuations and for the probability distribution of the
magnetization in the one-dimensional Ising model. The scaling functions are
evaluated in the limit of the temperature going to zero (T -> 0), the size of
the system going to infinity (N -> oo) while N[1-tanh(J/k_BT)] is kept finite
(J being the nearest neighbor coupling). Exact calculations using various
boundary conditions (periodic, antiperiodic, free, block) demonstrate
explicitly how the scaling functions depend on the boundary conditions. We also
show that the block (small part of a large system) magnetization distribution
results are identical to those obtained for free boundary conditions.Comment: 8 pages, 5 figure
Tricritical behaviour of Ising spin glasses with charge fluctuations
We show that tricritical points displaying unusal behaviour exist in phase
diagrams of fermionic Ising spin glasses as the chemical potential or the
filling assumes characteristic values. Exact results for infinite range
interaction and a one loop renormalization group analysis of thermal
tricritical fluctuations for finite range models are presented. Surprising
similarities with zero temperature transitions and a new tricritical
point of metallic quantum spin glasses are derived.Comment: 4 pages, 1 Postscript figure, minor change
Exact partition functions of the Ising model on MxN planar lattices with periodic-aperiodic boundary conditions
The Grassmann path integral approach is used to calculate exact partition
functions of the Ising model on MxN square (sq), plane triangular (pt) and
honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic
(pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary
conditions. The partition functions are used to calculate and plot the specific
heat, , as a function of the temperature, . We find that
for the NxN sq lattice, for pa and ap boundary conditions are different
from those for aa boundary conditions, but for the NxN pt and hc lattices,
for ap, pa, and aa boundary conditions have the same values. Our exact
partition functions might also be useful for understanding the effects of
lattice structures and boundary conditions on critical finite-size corrections
of the Ising model.Comment: 17 pages, 13 Postscript figures, uses iopams.sty, submitted to J.
Phys. A: Math. Ge
Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory
Due to recent successes of a statistical-based nonlocal continuum crystal
plasticity theory for single-glide in explaining various aspects such as
dislocation patterning and size-dependent plasticity, several attempts have
been made to extend the theory to describe crystals with multiple slip systems
using ad-hoc assumptions. We present here a mesoscale continuum theory of
plasticity for multiple slip systems of parallel edge dislocations. We begin by
constructing the Bogolyubov-Born-Green-Yvon-Kirkwood (BBGYK) integral equations
relating different orders of dislocation correlation functions in a grand
canonical ensemble. Approximate pair correlation functions are obtained for
single-slip systems with two types of dislocations and, subsequently, for
general multiple-slip systems of both charges. The effect of the correlations
manifests itself in the form of an entropic force in addition to the external
stress and the self-consistent internal stress. Comparisons with a previous
multiple-slip theory based on phenomenological considerations shall be
discussed.Comment: 12 pages, 3 figure
Ground State Structure in a Highly Disordered Spin Glass Model
We propose a new Ising spin glass model on of Edwards-Anderson type,
but with highly disordered coupling magnitudes, in which a greedy algorithm for
producing ground states is exact. We find that the procedure for determining
(infinite volume) ground states for this model can be related to invasion
percolation with the number of ground states identified as , where
is the number of distinct global components in the
``invasion forest''. We prove that if the invasion
connectivity function is square summable. We argue that the critical dimension
separating and is . When , we consider free or periodic boundary conditions on cubes of
side length and show that frustration leads to chaotic dependence with
{\it all} pairs of ground states occuring as subsequence limits. We briefly
discuss applications of our results to random walk problems on rugged
landscapes.Comment: LaTex fil
Small doubling in groups
Let A be a subset of a group G = (G,.). We will survey the theory of sets A
with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}.
The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos
Centenary conferenc
Magnetic field induced 3D to 1D crossover in type II superconductors
We review and analyze magnetization and specific heat investigations on
type-II superconductors which uncover remarkable evidence for the magnetic
field induced fnite size effect and the associated 3D to 1D crossover which
enhances thermal fluctuations.Comment: 26 pages, 19 figure
Continuum Model for River Networks
The effects of erosion, avalanching and random precipitation are captured in
a simple stochastic partial differential equation for modelling the evolution
of river networks. Our model leads to a self-organized structured landscape and
to abstraction and piracy of the smaller tributaries as the evolution proceeds.
An algebraic distribution of the average basin areas and a power law
relationship between the drainage basin area and the river length are found.Comment: 9 pages, Revtex 3.0, 7 figures in compressed format using uufiles
command, to appear in Phys. Rev. Lett., for an hard copy or problems e-mail
to [email protected]
Dipolar Excitons, Spontaneous Phase Coherence, and Superfluid-Insulator Transition in Bi-layer Quantum Hall Systems at
The spontaneous interlayer phase coherent (111) state of bi-layer Quantum
Hall system at filling factor may be viewed as a condensate of
interlayer particle-hole pairs or excitons. We show in this paper that when the
layers are biased in such a way that these excitons are very dilute, they may
be viewed as point-like bosons. We calculate the exciton dispersion relation,
and show that the exciton-exciton interaction is dominated by the dipole moment
they carry. In addition to the phase coherent state, we also find a Wigner
Crystal/Glass phase in the presence/absence of disorder which is an insulating
state for the excitons. The position of the phase boundary is estimated and the
properties of the superfluid-insulator type transition between these two phases
is discussed. We also discuss the relation between these "dipolar" excitons and
the "dipolar" composite fermions studied in the context of half-filled Landau
level.Comment: 4 pages with one embedded eps figur
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