# Glassy Critical Points and Random Field Ising Model

### Silvio Franz 1, Giorgio Parisi 2, Federico Ricci-Tersenghi 2

#### Journal of Statistical Mechanics (2013) L02001

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory describing these points can be mapped in the $\phi^4$-Random Field Ising Model. We confirm our analysis studying the finite size scaling of the $p$-spin model defined on sparse random graph, where a fraction of variables is frozen such that the phase transition is of a continuous kind.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza