20 research outputs found
Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
Geometrically frustrated materials have a ground-state degeneracy that may be
lifted by subtle effects, such as higher order interactions causing small
energetic preferences for ordered structures. Alternatively, ordering may
result from entropic differences between configurations in an effect termed
order-by-disorder. Motivated by recent experiments in a frustrated colloidal
system in which ordering is suspected to result from entropy, we consider in
this paper, the antiferromagnetic Ising model on a deformable triangular
lattice. We calculate the displacements exactly at the microscopic level, and
contrary to previous studies, find a partially disordered ground state of
randomly zigzagging stripes. Each such configuration is deformed differently
and thus has a unique phonon spectrum with distinct entropy, thus lifting the
degeneracy at finite temperature. Nonetheless, due to the free-energy barriers
between the ground-state configurations, the system falls into a disordered
glassy state.Comment: Accepted to PNA
Topological defects produce exotic mechanics in complex metamaterials
Biological and Soft Matter Physic
A note on the violation of the Einstein relation in a driven moderately dense granular gas
The Einstein relation for a driven moderately dense granular gas in
-dimensions is analyzed in the context of the Enskog kinetic equation. The
Enskog equation neglects velocity correlations but retains spatial correlations
arising from volume exclusion effects. As expected, there is a breakdown of the
Einstein relation relating diffusion and
mobility , being the temperature of the impurity. The kinetic theory
results also show that the violation of the Einstein relation is only due to
the strong non-Maxwellian behavior of the reference state of the impurity
particles. The deviation of from unity becomes more significant as
the solid volume fraction and the inelasticity increase, especially when the
system is driven by the action of a Gaussian thermostat. This conclusion
qualitatively agrees with some recent simulations of dense gases [Puglisi {\em
et al.}, 2007 {\em J. Stat. Mech.} P08016], although the deviations observed in
computer simulations are more important than those obtained here from the
Enskog kinetic theory. Possible reasons for the quantitative discrepancies
between theory and simulations are discussed.Comment: 6 figure
Current large deviations in a driven dissipative model
We consider lattice gas diffusive dynamics with creation-annihilation in the
bulk and maintained out of equilibrium by two reservoirs at the boundaries.
This stochastic particle system can be viewed as a toy model for granular gases
where the energy is injected at the boundary and dissipated in the bulk. The
large deviation functional for the particle currents flowing through the system
is computed and some physical consequences are discussed: the mechanism for
local current fluctuations, dynamical phase transitions, the
fluctuation-relation
Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models
Kinetically constrained models (KCMs) have been used to study and understand
the origin of glassy dynamics. Despite having trivial thermodynamic properties,
their dynamics slows down dramatically at low temperatures while displaying
dynamical heterogeneity as seen in glass forming supercooled liquids. This
dynamics has its origin in an ergodic-nonergodic first-order phase transition
between phases of distinct dynamical "activity". This is a "space-time"
transition as it corresponds to a singular change in ensembles of trajectories
of the dynamics rather than ensembles of configurations. Here we extend these
ideas to driven glassy systems by considering KCMs driven into non-equilibrium
steady states through non-conservative forces. By classifying trajectories
through their entropy production we prove that driven KCMs also display an
analogous first-order space-time transition between dynamical phases of finite
and vanishing entropy production. We also discuss how trajectories with rare
values of entropy production can be realized as typical trajectories of a
mapped system with modified forces
Response evolution of mechanical metamaterials under architectural transformations
Biological and Soft Matter Physic