466 research outputs found
Long-range interactions and non-extensivity in ferromagnetic spin models
The Ising model with ferromagnetic interactions that decay as is
analyzed in the non-extensive regime , where the
thermodynamic limit is not defined. In order to study the asymptotic properties
of the model in the limit ( being the number of spins)
we propose a generalization of the Curie-Weiss model, for which the
limit is well defined for all . We
conjecture that mean field theory is {\it exact} in the last model for all
. This conjecture is supported by Monte Carlo heat bath
simulations in the case. Moreover, we confirm a recently conjectured
scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive
() and non-extensive () regimes.Comment: RevTex, 12 pages, 1 eps figur
Correlations in Ising chains with non-integrable interactions
Two-spin correlations generated by interactions which decay with distance r
as r^{-1-sigma} with -1 <sigma <0 are calculated for periodic Ising chains of
length L. Mean-field theory indicates that the correlations, C(r,L), diminish
in the thermodynamic limit L -> \infty, but they contain a singular structure
for r/L -> 0 which can be observed by introducing magnified correlations,
LC(r,L)-\sum_r C(r,L). The magnified correlations are shown to have a scaling
form F(r/L) and the singular structure of F(x) for x->0 is found to be the same
at all temperatures including the critical point. These conclusions are
supported by the results of Monte Carlo simulations for systems with sigma
=-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc.Comment: 13 pages, latex, 5 eps figures in a separate uuencoded file, to
appear in Phys.Rev.
Patterns of silver eel (Anguilla anguilla L.) sex ratio in a catchment
Changes in the numbers and size-class structure of European silver eels, Anguilla anguilla, in the River Fre´mur (France) were examined over a 9-year period after installation of downstream eel passes. The number of silver eels migrating downstream peaked in 1999, then decreased strongly and steadily after 2000, reaching relatively low levels. At the same time, a gradual shift in the silver eel sex ratio from a dominance of males (size from 270 to 442 mm, age from 3 to 6 years) to females (size from 366 to 1112 mm, age from 4 to 9 years) was recorded. Possible explanations for the escapement patterns observed are environmental sex determination and the installation of eel passes on the main hydraulic engineering structures in 1992 and 1996
Orientational Ordering in Spatially Disordered Dipolar Systems
This letter addresses basic questions concerning ferroelectric order in
positionally disordered dipolar materials. Three models distinguished by dipole
vectors which have one, two or three components are studied by computer
simulation. Randomly frozen and dynamically disordered media are considered. It
is shown that ferroelectric order is possible in spatially random systems, but
that its existence is very sensitive to the dipole vector dimensionality and
the motion of the medium. A physical analysis of our results provides
significant insight into the nature of ferroelectric transitions.Comment: 4 pages twocolumn LATEX style. 4 POSTSCRIPT figures available from
[email protected]
Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma
Vortices in thin-film superconductors are often modelled as a system of
particles interacting via a repulsive logarithmic potential. Arguments are
presented to show that the hypothetical (Abrikosov) crystalline state for such
particles is unstable at any finite temperature against proliferation of
screened disclinations. The correlation length of crystalline order is
predicted to grow as as the temperature is reduced to zero, in
excellent agreement with our simulations of this two-dimensional system.Comment: 3 figure
Canonical Solution of Classical Magnetic Models with Long-Range Couplings
We study the canonical solution of a family of classical spin
models on a generic -dimensional lattice; the couplings between two spins
decay as the inverse of their distance raised to the power , with
. The control of the thermodynamic limit requires the introduction of
a rescaling factor in the potential energy, which makes the model extensive but
not additive. A detailed analysis of the asymptotic spectral properties of the
matrix of couplings was necessary to justify the saddle point method applied to
the integration of functions depending on a diverging number of variables. The
properties of a class of functions related to the modified Bessel functions had
to be investigated. For given , and for any , and lattice
geometry, the solution is equivalent to that of the model, where the
dimensionality and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic
Magnetization distribution in the transverse Ising chain with energy flux
The zero-temperature transverse Ising chain carrying an energy flux j_E is
studied with the aim of determining the nonequilibrium distribution functions,
P(M_z) and P(M_x), of its transverse and longitudinal magnetizations,
respectively. An exact calculation reveals that P(M_z) is a Gaussian both at
j_E=0 and j_E not equal 0, and the width of the distribution decreases with
increasing energy flux. The distribution of the order-parameter fluctuations,
P(M_x), is evaluated numerically for spin-chains of up to 20 spins. For the
equilibrium case (j_E=0), we find the expected Gaussian fluctuations away from
the critical point while the critical order-parameter fluctuations are shown to
be non-gaussian with a scaling function Phi(x)=Phi(M_x/)=P(M_x)
strongly dependent on the boundary conditions. When j_E not equal 0, the system
displays long-range, oscillating correlations but P(M_x) is a Gaussian
nevertheless, and the width of the Gaussian decreases with increasing j_E. In
particular, we find that, at critical transverse field, the width has a
j_E^(-3/8) asymptotic in the j_E -> 0 limit.Comment: 8 pages, 5 ps figure
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