539 research outputs found
On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals
The dynamic and kinetic behavior of processes occurring in fractals with
spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the
existence of a fundamental scaling ratio (b_1). We address time-dependent
physical processes, which as a consequence of the time evolution develop a
characteristic length of the form , where z is the dynamic
exponent. So, we conjecture that the interplay between the physical process and
the symmetry properties of the fractal leads to the occurrence of time DSI
evidenced by soft log-periodic modulations of physical observables, with a
fundamental time scaling ratio given by . The conjecture is
tested numerically for random walks, and representative systems of broad
universality classes in the fields of irreversible and equilibrium critical
phenomena.Comment: 6 pages, 3 figures. Submitted to EP
Diffusive Thermal Dynamics for the Ising Ferromagnet
We introduce a thermal dynamics for the Ising ferromagnet where the energy
variations occurring within the system exhibit a diffusive character typical of
thermalizing agents such as e.g. localized excitations. Time evolution is
provided by a walker hopping across the sites of the underlying lattice
according to local probabilities depending on the usual Boltzmann weight at a
given temperature. Despite the canonical hopping probabilities the walker
drives the system to a stationary state which is not reducible to the canonical
equilibrium state in a trivial way. The system still exhibits a magnetic phase
transition occurring at a finite value of the temperature larger than the
canonical one. The dependence of the model on the density of walkers realizing
the dynamics is also discussed. Interestingly the differences between the
stationary state and the Boltzmann equilibrium state decrease with increasing
number of walkers.Comment: 9 pages, 14 figures. Accepted for publication on PR
On the center of mass of Ising vectors
We show that the center of mass of Ising vectors that obey some simple
constraints, is again an Ising vector.Comment: 8 pages, 3 figures, LaTeX; Claims in connection with disordered
systems have been withdrawn; More detailed description of the simulations;
Inset added to figure
Spin-spin interaction and spin-squeezing in an optical lattice
We show that by displacing two optical lattices with respect to each other,
we may produce interactions similar to the ones describing ferro-magnetism in
condensed matter physics. We also show that particularly simple choices of the
interaction lead to spin-squeezing, which may be used to improve the
sensitivity of atomic clocks. Spin-squeezing is generated even with partially,
and randomly, filled lattices, and our proposal may be implemented with current
technology.Comment: 4 pages, including 4 figure
Integrable field theory and critical phenomena. The Ising model in a magnetic field
The two-dimensional Ising model is the simplest model of statistical
mechanics exhibiting a second order phase transition. While in absence of
magnetic field it is known to be solvable on the lattice since Onsager's work
of the forties, exact results for the magnetic case have been missing until the
late eighties, when A.Zamolodchikov solved the model in a field at the critical
temperature, directly in the scaling limit, within the framework of integrable
quantum field theory. In this article we review this field theoretical approach
to the Ising universality class, with particular attention to the results
obtained starting from Zamolodchikov's scattering solution and to their
comparison with the numerical estimates on the lattice. The topics discussed
include scattering theory, form factors, correlation functions, universal
amplitude ratios and perturbations around integrable directions. Although we
restrict our discussion to the Ising model, the emphasis is on the general
methods of integrable quantum field theory which can be used in the study of
all universality classes of critical behaviour in two dimensions.Comment: 42 pages; invited review article for J. Phys.
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
Analysing and controlling the tax evasion dynamics via majority-vote model
Within the context of agent-based Monte-Carlo simulations, we study the
well-known majority-vote model (MVM) with noise applied to tax evasion on
simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert
networks, and Erd\"os-R\'enyi random graphs. In the order to analyse and to
control the fluctuations for tax evasion in the economics model proposed by
Zaklan, MVM is applied in the neighborhod of the noise critical . The
Zaklan model had been studied recently using the equilibrium Ising model. Here
we show that the Zaklan model is robust and can be reproduced also through the
nonequilibrium MVM on various topologies.Comment: 18 pages, 7 figures, LAWNP'09, 200
On universality in aging ferromagnets
This work is a contribution to the study of universality in
out-of-equilibrium lattice models undergoing a second-order phase transition at
equilibrium. The experimental protocol that we have chosen is the following:
the system is prepared in its high-temperature phase and then quenched at the
critical temperature . We investigated by mean of Monte Carlo simulations
two quantities that are believed to take universal values: the exponent
obtained from the decay of autocorrelation functions and the
asymptotic value of the fluctuation-dissipation ratio . This
protocol was applied to the Ising model, the 3-state clock model and the
4-state Potts model on square, triangular and honeycomb lattices and to the
Ashkin-Teller model at the point belonging at equilibrium to the 3-state Potts
model universality class and to a multispin Ising model and the Baxter-Wu model
both belonging to the 4-state Potts model universality class at equilibrium.Comment: 17 page
Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem
We present a detailed description of the idea and procedure for the newly
proposed Monte Carlo algorithm of tuning the critical point automatically,
which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and
Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we
investigate the three-dimensional Ising model and the bond percolation problem.
We employ a refined finite-size scaling analysis to make estimates of critical
point and exponents. With much less efforts, we obtain the results which are
consistent with the previous calculations. We argue several directions for the
application of the PCC algorithm.Comment: 6 pages including 8 eps figures, to appear in J. Phys. Soc. Jp
Scaling Limit of the Ising Model in a Field
The dilute A_3 model is a solvable IRF (interaction round a face) model with
three local states and adjacency conditions encoded by the Dynkin diagram of
the Lie algebra A_3. It can be regarded as a solvable version of an Ising model
at the critical temperature in a magnetic field. One therefore expects the
scaling limit to be governed by Zamolodchikov's integrable perturbation of the
c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz
approach succeeded to unveil the corresponding E_8 structure under certain
assumptions on the nature of the Bethe Ansatz solutions. In order to check
these conjectures, we perform a detailed numerical investigation of the
solutions of the Bethe Ansatz equations for the critical and off-critical
model. Scaling functions for the ground-state corrections and for the lowest
spectral gaps are obtained, which give very precise numerical results for the
lowest mass ratios in the massive scaling limit. While these agree perfectly
with the E_8 mass ratios, we observe one state which seems to violate the
assumptions underlying the thermodynamic Bethe Ansatz calculation. We also
analyze the critical spectrum of the dilute A_3 model, which exhibits massive
excitations on top of the massless states of the Ising conformal field theory.Comment: 29 pages, RevTeX, 11 PostScript figures included by epsf, using
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