Transition in coupled replicas may not imply a finite-temperature ideal glass transition in glass-forming systems

A key open question in the glass transition field is whether a finite temperature thermodynamic transition to the glass state exists or not. Recent simulations of coupled replicas in atomistic models have found signatures of a static transition as a function of replica coupling. This can be viewed as evidence of an associated thermodynamic glass transition in the uncoupled system. We demonstrate here that a different interpretation is possible. We consider the triangular plaquette model, an interacting spin system which displays (East model-like) glassy dynamics in the absence of any static transition. We show that when two replicas are coupled, there is a curve of equilibrium phase transitions, between phases of small and large overlap, in the temperature-coupling plane (located on the self-dual line of an exact temperature-coupling duality of the system) which ends at a critical point. Crucially, in the limit of vanishing coupling the finite temperature transition disappears, and the uncoupled system is in the disordered phase at all temperatures. We discuss an interpretation of atomistic simulations in light of this result.

Figure 1

Exact phase diagram of two coupled triangular plaquette glass models. The temperature $T$ and coupling $\epsilon$ are in units of the energy constant of the model, $J$. The full line is a curve of first-order transitions from a phase with low overlap between the replicas to a phase of high overlap between the replicas. The transition line $\overline{T}\left(\varepsilon \right)$ is on the self-dual curve of the model (dashed line) and ends at a critical point $({\varepsilon }_{\mathrm{c}}/J,T_{\mathrm{c}}/J)=[1,1/ln(1+\sqrt{2})]$. The phase transition disappears in the limit of vanishing coupling, $\overline{T}(\varepsilon \to 0)=0$, and there is no finite $T$ singularity in the uncoupled system.