40 research outputs found
One-dimensional Kac model of dense amorphous hard spheres
We introduce a new model of hard spheres under confinement for the study of
the glass and jamming transitions. The model is an one-dimensional chain of the
-dimensional boxes each of which contains the same number of hard spheres,
and the particles in the boxes of the ends of the chain are quenched at their
equilibrium positions. We focus on the infinite dimensional limit () of the model and analytically compute the glass transition densities
using the replica liquid theory. From the chain length dependence of the
transition densities, we extract the characteristic length scales at the glass
transition. The divergence of the lengths are characterized by the two
exponents, for the dynamical transition and for the ideal glass
transition, which are consistent with those of the -spin mean-field spin
glass model. We also show that the model is useful for the study of the growing
length scale at the jamming transition.Comment: 6 pages, 4 figure
Effect of particle exchange on the glass transition of binary hard spheres
We investigate the replica theory of the liquid-glass transition for a binary
mixture of large and small additive hard spheres. We consider two different
ans\"atze for this problem: the frozen glass ansatz (FGA) in whichs the
exchange of large and small particles in a glass state is prohibited, and the
exchange glass ansatz (EGA), in which it is allowed. We calculate the dynamical
and thermodynamical glass transition points with the two ans\"atze. We show
that the dynamical transition density of the FGA is lower than that of the EGA,
while the thermodynamical transition density of the FGA is higher than that of
the EGA. We discuss the algorithmic implications of these results for the
density-dependence of the relaxation time of supercooled liquids. We
particularly emphasize the difference between the standard Monte Carlo and swap
Monte Carlo algorithms. Furthermore, we discuss the importance of particle
exchange for estimating the configurational entropy.Comment: 16 pages, 5 figure
Fredrickson-Andersen model on Bethe lattice with random pinning
We study the effects of random pinning on the Fredrickson-Andersen model on
the Bethe lattice. We find that the nonergodic transition temperature rises as
the fraction of the pinned spins increases and the transition line terminates
at a critical point. The freezing behavior of the spins is analogous to that of
a randomly pinned p-spin mean-field spin glass model which has been recently
reported. The diverging behavior of correlation lengths in the vicinity of the
terminal critical point is found to be identical to the prediction of the
inhomogeneous mode-coupling theory at the A3 singularity point for the glass
transition.Comment: 6 pages, 7 figure
Correlated Noise and Critical Dimensions
In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry
breaking for all dimensions . In this work, we discuss that this
limitation can be circumvented in non-equilibrium systems driven by the
spatio-temporally long-range anticorrelated noise. We first compute the lower
and upper critical dimensions of the model driven by the
spatio-temporally correlated noise by means of the dimensional analysis. Next,
we consider the spherical model, which corresponds to the large limit of
the model and allows us to compute the critical dimensions and critical
exponents, analytically. Both results suggest that the critical dimensions
increase when the noise is positively correlated in space and time, and
decrease when anticorrelated. We also report that the spherical model with the
correlated noise shows the hyperuniformity and giant number fluctuation even
well above the critical point.Comment: 7 page