Jamming and Glass Transitions: In Mean-Field Theories and Beyond

Description

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 important connections among constraint satisfaction problems, jamming and critical phenomena in complex systems, and lay part of the groundwork for a complete theory of amorphous solids. Front Matter ....Pages i-xxi Introduction (Ada Altieri)....Pages 1-6 Front Matter ....Pages 7-7 Supercooled Liquids and the Glass Transition (Ada Altieri)....Pages 9-43 The Jamming Transition (Ada Altieri)....Pages 45-64 An Exactly Solvable Model: The Perceptron (Ada Altieri)....Pages 65-113 Universality Classes: Perceptron Versus Sphere Models (Ada Altieri)....Pages 115-131 The Jamming Paradigm in Ecology (Ada Altieri)....Pages 133-152 Front Matter ....Pages 153-153 The M-Layer Construction (Ada Altieri)....Pages 155-189 Front Matter ....Pages 191-191 Conclusions and Perspectives (Ada Altieri)....Pages 193-198 Back Matter ....Pages 199-220