Activated dynamics at a non-disordered critical point

– We present a non-randomly, frustrated lattice model which exhibits activated dynamics at a critical point. The phase transition involves ordering of large-scale structures which occur naturally within the model. Through the construction of a coarse-grained master equation, we show that the time scales diverge exponentially while the static fluctuations exhibit the usual power law divergences. We discuss the relevance of this scenario in the context of the glass transition in supercooled liquids. One of the most striking features of supercooled liquids approaching the glass transition is a precipitous slowing down of the dynamics with no obvious structural changes. Relaxation times are observed to grow by more than ten orders of magnitude as the temperature is decreased by less than a factor of two [1]. A natural explanation of this exponential growth, often quantified by the Vogel-Fulcher-Tammann (VFT) formula [2], is the existence of a critical point with diverging free-energy barriers. This scenario is explicitly realized in the random field Ising model [3], and a scaling theory of the glass transition has been proposed based on the existence of such a critical point [4]. However, an explicit realization of this scenario in a model with no quenched-in disorder has, to our knowledge, not been demonstrated. The VFT form itself has been obtained from a scaling analysis of a diffusion-deposition model [5] Another piece of the glass puzzle, the presence of dynamical heterogeneities —large clusters of fast moving particles— was uncovered recently near the glass transition in experiments on colloids [6] and in simulations of Lennard-Jones liquids [7]. Inspired by the questions raised by recent experiments, we have investigated a non-disordered, frustrated, lattice model which exhibits activated dynamics at a critical point, and where the diverging barriers arise from extended spatial structures. Over the years, different theories of the glass transition have highlighted different aspects of the problem. The frustration-limited domain theory [1,8] relates the activated nature of the dynamics to a critical point “avoided” due to frustration imposed by competing interactions. The random first-order transition theory [9] relies on the presence of frustration in glass formers to provide for an extensive number of metastable states, which are responsible for the dynamical behavior observed near the glass transition. A very different perspective on the glass transition is provided by the mode coupling theory which predicts a purely dynamical critical