Random-field Ising-like effective theory of the glass transition. I. Mean-field models

Almost any liquid when cooled fast enough forms an amorphous solid, called a glass. Here, the authors develop an effective theory of the glass transition that is able to include nonperturbative fluctuations due to self-induced disorder. Their approach allows a reformulation of the problem in terms of simpler models originally introduced to describe disordered magnetic systems. The authors discuss the physical implications of such a mapping, including the possibility to determine the existence or not of an underlying finite-temperature thermodynamic glass transition in supercooled liquids.