© 2019

Jamming and Glass Transitions

In Mean-Field Theories and Beyond


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Ada Altieri
    Pages 1-6
  3. Glass and Jamming Transitions in Mean-Field Models

    1. Front Matter
      Pages 7-7
    2. Ada Altieri
      Pages 45-64
    3. Ada Altieri
      Pages 133-152
  4. Lattice Theories Beyond Mean-Field

    1. Front Matter
      Pages 153-153
    2. Ada Altieri
      Pages 155-189
  5. Conclusions

    1. Front Matter
      Pages 191-191
    2. Ada Altieri
      Pages 193-198
  6. Back Matter
    Pages 199-220

About this book


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.


Disordered and Glassy Systems Jamming Transition Constraint Satisfaction Problems Perceptron Model SAT/UNSAT Transition Thouless-Anderson-Palmer Equations Plefka Expansion Loop Expansion on the Bethe Lattice Bethe M-layer MacArthur Model

Authors and affiliations

  1. 1.Département de PhysiqueÉcole Normale SupérieureParisFrance

Bibliographic information