3,895 research outputs found
Critical behavior of an Ising model with aperiodic interactions
We write exact renormalization-group recursion relations for a ferromagnetic
Ising model on the diamond hierarchical lattice with an aperiodic distribution
of exchange interactions according to a class of generalized two-letter
Fibonacci sequences. For small geometric fluctuations, the critical behavior is
unchanged with respect to the uniform case. For large fluctuations, the uniform
fixed point in the parameter space becomes fully unstable. We analyze some
limiting cases, and propose a heuristic criterion to check the relevance of the
fluctuations.Comment: latex file, 5 figures, accepted by Braz. Jour. Phy
Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model
We investigate the phase diagram of a spin- Ising model on a cubic
lattice, with competing interactions between nearest and next-nearest neighbors
along an axial direction, and fully connected spins on the sites of each
perpendicular layer. The problem is formulated in terms of a set of
noninteracting Ising chains in a position-dependent field. At low temperatures,
as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising
(ANNNI) model, there are many distinct spatially commensurate phases that
spring from a multiphase point of infinitely degenerate ground states. As
temperature increases, we confirm the existence of a branching mechanism
associated with the onset of higher-order commensurate phases. We check that
the ferromagnetic phase undergoes a first-order transition to the modulated
phases. Depending on a parameter of competition, the wave number of the striped
patterns locks in rational values, giving rise to a devil's staircase. We
numerically calculate the Hausdorff dimension associated with these
fractal structures, and show that increases with temperature but seems
to reach a limiting value smaller than .Comment: 17 pages, 6 figure
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
A thermodynamical fiber bundle model for the fracture of disordered materials
We investigate a disordered version of a thermodynamic fiber bundle model
proposed by Selinger, Wang, Gelbart, and Ben-Shaul a few years ago. For simple
forms of disorder, the model is analytically tractable and displays some new
features. At either constant stress or constant strain, there is a non
monotonic increase of the fraction of broken fibers as a function of
temperature. Moreover, the same values of some macroscopic quantities as stress
and strain may correspond to different microscopic cofigurations, which can be
essential for determining the thermal activation time of the fracture. We argue
that different microscopic states may be characterized by an experimentally
accessible analog of the Edwards-Anderson parameter. At zero temperature, we
recover the behavior of the irreversible fiber bundle model.Comment: 18 pages, 10 figure
The fluctuation-dissipation theorem and the linear Glauber model
We obtain exact expressions for the two-time autocorrelation and response
functions of the -dimensional linear Glauber model. Although this linear
model does not obey detailed balance in dimensions , we show that the
usual form of the fluctuation-dissipation ratio still holds in the stationary
regime. In the transient regime, we show the occurence of aging, with a special
limit of the fluctuation-dissipation ratio, , for a quench at
the critical point.Comment: Accepted for publication (Physical Review E
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