Jamming and Glass Transitions

The work described in this book originates from a major effort to develop a fundamental theory of the glass and the jamming transitions.

The first chapters guide the reader through the phenomenology of supercooled liquids and structural glasses and provide the tools to analyze the most frequently used models able to predict the complex behavior of such systems. A fundamental outcome is a detailed theoretical derivation of an effective thermodynamic potential, along with the study of anomalous vibrational properties of sphere systems. The interested reader can find in these pages a clear and deep analysis of mean-field models as well as the description of advanced beyond-mean-field perturbative expansions. To investigate important second-order phase transitions in lattice models, the last part of the book proposes an innovative theoretical approach, based on a multi-layer construction.

The different methods developed in this thesis shed new light on importantconnections among constraint satisfaction problems, jamming and critical phenomena in complex systems, and lay part of the groundwork for a complete theory of amorphous solids.

Nominated as an outstanding Ph.D. thesis by the Sapienza University, Rome, Italy Offers a detailed overview of supercooled liquids and glassy systems Explains every facet of the jamming paradigm and its connections with an archetype model of learning, the perceptron Provides advanced analytical techniques both in high-dimensional systems and in lattice models

Contenu
Introduction.- Glass and jamming transitions in mean-eld models.- Supercooled liquids and the glass transition.- The Jamming Transition.- An Exactly Solvable Model: The Perceptron.- Universality Classes: Perceptron Versus Sphere Models.- The Jamming Paradigm in Ecology.- Lattice Theories Beyond Mean-eld.- The M- layer construction.- Conclusions.- Conclusions and Perspectives.- Appendix.