Non-Universality of the Specific Heat in Glass Forming Systems

We present new simulation results for the specific heat in a classical model of a binary mixture glass-former in two dimensions. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. This is a surprise, as most texts on the glass transition expect a single specific heat peak. We explain the physics of the two specific heat peaks by the micro-melting of two types of clusters. While this physics is easily accessible, the consequences are that one should not expect any universality in the temperature dependence of the specific heat in glass formers

Anisotropic Diffusion Limited Aggregation

Using stochastic conformal mappings we study the effects of anisotropic perturbations on diffusion limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant measure on a unit circle. Here we map $m$ preferred directions for growth of angular width $\sigma$ to a distribution on the unit circle which is a periodic function with $m$ peaks in $[-\pi, \pi)$ such that the width $\sigma$ of each peak scales as $\sigma \sim 1/\sqrt{k}$, where $k$ defines the ``strength'' of anisotropy along any of the $m$ chosen directions. The two parameters $(m,k)$ map out a parameter space of perturbations that allows a continuous transition from DLA (for $m=0$ or $k=0$) to $m$ needle-like fingers as $k \to \infty$. We show that at fixed $m$ the effective fractal dimension of the clusters $D(m,k)$ obtained from mass-radius scaling decreases with increasing $k$ from $D_{DLA} \simeq 1.71$ to a value bounded from below by $D_{min} = 3/2$. Scaling arguments suggest a specific form for the dependence of the fractal dimension $D(m,k)$ on $k$ for large $k$, form which compares favorably with numerical results.Comment: 6 pages, 4 figures, submitted to Phys. Rev.

Do Athermal Amorphous Solids Exist?

We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of non-affine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B_2 has anomalous fluctuations and the second nonlinear coefficient B_3 and all the higher order coefficients (which are non-zero by symmetry) diverge in the thermodynamic limit. These results put a question mark on the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.Comment: 11 pages, 11 figure