193 research outputs found
Replica theory of the rigidity of structural glasses
We present a first principle scheme to compute the rigidity, i. e. the
shear-modulus of structural glasses at finite temperatures using the cloned
liquid theory, which combines the replica theory and the liquid theory. With
the aid of the replica method which enables disentanglement of thermal
fluctuations in liquids into intra-state and inter-state fluctuations, we
extract the rigidity of metastable amorphous solid states in the supercooled
liquid and glass phases. The result can be understood intuitively without
replicas. As a test case, we apply the scheme to the supercooled and glassy
state of a binary mixture of soft-spheres. The result compares well with the
shear-modulus obtained by a previous molecular dynamic simulation. The rigidity
of metastable states is significantly reduced with respect to the instantaneous
rigidity, namely the Born term, due to non-affine responses caused by
displacements of particles inside cages at all temperatures down to T=0. It
becomes nearly independent of temperature below the Kauzmann temperature T_K.
At higher temperatures in the supercooled liquid state, the non-affine
correction to the rigidity becomes stronger suggesting melting of the
metastable solid state. Inter-state part of the static response implies jerky,
intermittent stress-strain curves with static analogue of yielding at
mesoscopic scales.Comment: 52 pages, 10 figure
Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
We construct and analyze a family of -component vectorial spin systems
which exhibit glass transitions and jamming within supercooled paramagnetic
states without quenched disorder. Our system is defined on lattices with
connectivity and becomes exactly solvable in the limit of large
number of components . We consider generic -body interactions
between the vectorial Ising/continuous spins with linear/non-linear potentials.
The existence of self-generated randomness is demonstrated by showing that the
random energy model is recovered from a -component ferromagnetic -spin
Ising model in and limit. In our systems the
quenched disorder, if present, and the self-generated disorder act additively.
Our theory provides a unified mean-field theoretical framework for glass
transitions of rotational degree of freedoms such as orientation of molecules
in glass forming liquids, color angles in continuous coloring of graphs and
vector spins of geometrically frustrated magnets. The rotational glass
transitions accompany various types of replica symmetry breaking. In the case
of repulsive hardcore interactions in the spin space, continuous the
criticality of the jamming or SAT/UNSTAT transition becomes the same as that of
hardspheres.Comment: 85 pages (9 figures) Revised and extended version submitted to
SciPost Physics. (Analysis on anisotropic particles included in v2 will be
presented in a separate publication.
Rigidity of glasses and jamming systems at low temperatures
We discuss a microscopic scheme to compute the rigidity of glasses or the
plateau modulus of supercooled liquids by twisting replicated liquids. We first
summarize the method in the case of harmonic glasses with analytic potentials.
Then we discuss how it can be extended to the case of repulsive contact systems
: the hard sphere glass and related systems with repulsive contact potentials
which enable the jamming transition at zero temperature. For the repulsive
contact systems we find entropic rigidity which behaves similarly as the
pressure in the low temperature limit: it is proportional to the temperature
and tends to diverge approaching the jamming density with increasing volume
fraction, which may account for experimental observations of rigidities of
repulsive colloids and emulsions.Comment: 8 pages, submitted to AIP conference proceedings for "Slow Dynamics
in Complex Systems" (Sendai, Japan, Dec. 2012
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