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A key open question in the glass transition field is whether a finitetemperature thermodynamic transition to the glass state exists or not. Recentsimulations of coupled replicas in atomistic models have found signatures of astatic transition as a function of replica coupling. This can be viewed asevidence of an associated thermodynamic glass transition in the uncoupledsystem. We demonstrate here that a different interpretation is possible. Weconsider the triangular plaquette model, an interacting spin system whichdisplays (East model-like) glassy dynamics in the absence of any statictransition. We show that when two replicas are coupled there is a curve ofequilibrium phase transitions, between phases of small and large overlap, inthe temperature-coupling plane (located on the self-dual line of an exacttemperature/coupling duality of the system) which ends at a critical point.Crucially, in the limit of vanishing coupling the finite temperature transitiondisappears, and the uncoupled system is in the disordered phase at alltemperatures. We discuss interpretation of atomistic simulations in light ofthis result.

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