926 research outputs found
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
Multicritical behavior in the fully frustrated XY model and related systems
We study the phase diagram and critical behavior of the two-dimensional
square-lattice fully frustrated XY model (FFXY) and of two related models, a
lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the
critical modes of the FFXY model, and a coupled Ising-XY model. We present a
finite-size-scaling analysis of the results of high-precision Monte Carlo
simulations on square lattices L x L, up to L=O(10^3).
In the FFXY model and in the other models, when the transitions are
continuous, there are two very close but separate transitions. There is an
Ising chiral transition characterized by the onset of chiral long-range order
while spins remain paramagnetic. Then, as temperature decreases, the systems
undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range
order.
The FFXY model and the other models in a rather large parameter region show a
crossover behavior at the chiral and spin transitions that is universal to some
extent. We conjecture that this universal behavior is due to a multicritical
point. The numerical data suggest that the relevant multicritical point is a
zero-temperature transition. A possible candidate is the O(4) point that
controls the low-temperature behavior of the 4-vector model.Comment: 62 page
Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model
We analyse the spin wave approximation for the 2D-XY model, directly in
reciprocal space. In this limit the model is diagonal and the normal modes are
statistically independent. Despite this simplicity non-trivial critical
properties are observed and exploited. We confirm that the observed asymmetry
for the probability density function for order parameter fluctuations comes
from the divergence of the mode amplitudes across the Brillouin zone. We show
that the asymmetry is a many body effect despite the importance played by the
zone centre. The precise form of the function is dependent on the details of
the Gibbs measure, giving weight to the idea that an effective Gibbs measure
should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure
The New Political Economy of EU State Aid Policy
Despite its importance and singularity, the EU’s state aid policy has attracted less scholarly attention than other elements of EU competition policy. Introducing the themes addressed by the special issue, this article briefly reviews the development of EU policy and highlights why the control of state aid matters. The Commission’s response to the current economic crisis notably in banking and the car industry is a key concern, but the interests of the special issue go far beyond. They include: the role of the European Commission in the development of EU policy, the politics of state aid, and a clash between models of capitalism. The special issue also examines the impact of EU policy. It investigates how EU state aid decisions affect not only industrial policy at the national level (and therefore at the EU level), but the welfare state and territorial relations within federal member states, the external implications of EU action and the strategies pursued by the Commission to limit any potential disadvantage to European firms, and the conflict between the EU’s expanding legal order and national
Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?
Critical finite-size scaling functions for the order parameter distribution
of the two and three dimensional Ising model are investigated. Within a
recently introduced classification theory of phase transitions, the universal
part of the critical finite-size scaling functions has been derived by
employing a scaling limit that differs from the traditional finite-size scaling
limit. In this paper the analytical predictions are compared with Monte Carlo
simulations. We find good agreement between the analytical expression and the
simulation results. The agreement is consistent with the possibility that the
functional form of the critical finite-size scaling function for the order
parameter distribution is determined uniquely by only a few universal
parameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as
uuencoded gzipped tar file. To appear in J. Phys. A
Generalized Dynamic Scaling for Critical Magnetic Systems
The short-time behaviour of the critical dynamics for magnetic systems is
investigated with Monte Carlo methods. Without losing the generality, we
consider the relaxation process for the two dimensional Ising and Potts model
starting from an initial state with very high temperature and arbitrary
magnetization. We confirm the generalized scaling form and observe that the
critical characteristic functions of the initial magnetization for the Ising
and the Potts model are quite different.Comment: 32 pages with15 eps-figure
Wetting of a symmetrical binary fluid mixture on a wall
We study the wetting behaviour of a symmetrical binary fluid below the
demixing temperature at a non-selective attractive wall. Although it demixes in
the bulk, a sufficiently thin liquid film remains mixed. On approaching
liquid/vapour coexistence, however, the thickness of the liquid film increases
and it may demix and then wet the substrate. We show that the wetting
properties are determined by an interplay of the two length scales related to
the density and the composition fluctuations. The problem is analysed within
the framework of a generic two component Ginzburg-Landau functional
(appropriate for systems with short-ranged interactions). This functional is
minimized both numerically and analytically within a piecewise parabolic
potential approximation. A number of novel surface transitions are found,
including first order demixing and prewetting, continuous demixing, a
tricritical point connecting the two regimes, or a critical end point beyond
which the prewetting line separates a strongly and a weakly demixed film. Our
results are supported by detailed Monte Carlo simulations of a symmetrical
binary Lennard-Jones fluid at an attractive wall.Comment: submitted to Phys. Rev.
Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
The solutions of the time independent Schrodinger equation for non-Hermitian
(NH) Hamiltonians have been extensively studied and calculated in many
different fields of physics by using L^2 methods that originally have been
developed for the calculations of bound states. The existing non-Hermitian
formalism breaks down when dealing with wavepackets(WP). An open question is
how time dependent expectation values can be calculated when the Hamiltonian is
NH ? Using the F-product formalism, which was recently proposed, [J. Phys.
Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of
different observable quantities for a simple well known study test case model
Hamiltonian. We carry out a comparison between these results with those
obtained from conventional(i.e., Hermitian) quantum mechanics (QM)
calculations. The remarkable agreement between these results emphasizes the
fact that in the NH-QM, unlike standard QM, there is no need to split the
entire space into two regions; i.e., the interaction region and its
surrounding. Our results open a door for a type of WP propagation calculations
within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review
Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and non-exponential contributions
The buildup process of the probability density inside the quantum well of a
double-barrier resonant structure is studied by considering the analytic
solution of the time dependent Schr\"{o}dinger equation with the initial
condition of a cutoff plane wave. For one level systems at resonance condition
we show that the buildup of the probability density obeys a simple charging up
law, where is the
stationary wave function and the transient time constant is exactly
two lifetimes. We illustrate that the above formula holds both for symmetrical
and asymmetrical potential profiles with typical parameters, and even for
incidence at different resonance energies. Theoretical evidence of a crossover
to non-exponential buildup is also discussed.Comment: 4 pages, 2 figure
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