$p$-Spin Model in Finite Dimensions and Its Relation to Structural Glasses

The $p$-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly that the finite-dimensional version of the three-spin model is in the same universality class as an Ising spin glass in a magnetic field. Assuming that the droplet picture of Ising spin glasses is valid we discuss how this universality may provide insights into why structural glasses are either “fragile” or “strong.”

Figure 1

The correlation length of the three-spin model in three dimensions as a function of $T/J$, as obtained using the MKA.