29 research outputs found
Hard-needle elastomer in one spatial dimension
We perform exact Statistical Mechanics calculations for a system of elongated
objects (hard needles) that are restricted to translate along a line and rotate
within a plane, and that interact via both excluded-volume steric repulsion and
harmonic elastic forces between neighbors. This system represents a
one-dimensional model of a liquid crystal elastomer, and has a zero-tension
critical point that we describe using the transfer-matrix method. In the
absence of elastic interactions, we build on previous results by Kantor and
Kardar, and find that the nematic order parameter decays linearly with
tension . In the presence of elastic interactions, the system exhibits
a standard universal scaling form, with being a function of the
rescaled elastic energy constant , where is a
critical exponent equal to for this model. At zero tension, simple scaling
arguments lead to the asymptotic behavior , which does not
depend on the equilibrium distance of the springs in this model.Comment: 6 pages, 4 figures, to be submitted to a special issue in Brazilian
Journal of Physics in honor of Prof. Silvio R. Salina
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
Compressible Sherrington-Kirkpatrick spin-glass model
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of
elastic degrees of freedom. The problem is formulated in terms of an effective
four-spin Hamiltonian in the pressure ensemble, which can be treated by the
replica method. In the replica-symmetric approximation, we analyze the
pressure-temperature phase diagram, and obtain expressions for the critical
boundaries between the disordered and the ordered (spin-glass and
ferromagnetic) phases. The second-order para-ferromagnetic border ends at a
tricritical point, beyond which the transition becomes discontinuous. We use
these results to make contact with the temperature-concentration phase diagrams
of mixtures of hydrogen-bonded crystals.Comment: 8 pages, 2 figures; added references, added conten