Related papers: A model free energy for glasses
We consider the spherical Sherrington-Kirkpatrick model of spin glass with sparse interaction, where the interactions between most of the pairs of the spin variables are possibly zero. With suitable normalization, we prove that the limiting…
We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effects. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in…
Dynamics near the surface of glasses is generally much faster than in the bulk. Neglecting static perturbations of structure at the surface, we use random first order transition theory to show the free energy barrier for activated motion…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a…
We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this…
20 years ago, Bovier, Kurkova, and L\"owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we…
Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models,…
We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…
The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural…
An alternative scenario for the glass transition based on the cooperative nature of nucleation processes and the role of entropic effects is presented. The new ingredient is to relate the dissipation during the relaxation process to the…
The gauge principle as applied in field theories for particle physics recognizes redundant degrees of freedom. Some time ago this author introduced a frustration based locally preferred structure (LPS) model of the glass transition. Here we…
A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with…
We develop a free energy framework to describe the response of glasses to applied stress. Unlike crystals, for which the free energy increases quadratically with strain due to affine displacements, for glasses, the nonequilibrium free…
We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra…
We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations.…
We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…
We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments…
Despite the critical importance of the elastic properties of modern materials, there is not a singular model that can predict the modulus to an accuracy needed for industrial glass design. To address this problem, we propose an approach to…
In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are…