Glassy critical points and the random field Ising model

We consider the critical properties of points of the continuous glass transition that one can find in liquids in the 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 ϕ 4 -random field Ising model. We confirm our analysis by studying the finite size scaling of the p-spin model defined on a sparse random graph, where a fraction of the variables are frozen such that the phase transition is of a continuous kind.