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Introduction
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The dynamics of supercooled liquids approaching the glass transition remains one of the most fundamental problems in condensed matter physics [@review]. Some of the prominent dynamic features in supercooled liquids include the enormous increase in relaxation time scale with lowering temperature, and the nonexponential relaxation in the response to an external perturbation. In addition to these features, an anomaly in transport properties such as breakdown of the Stokes-Einstein (SE) relation in highly supercooled liquids has been observed in experiments [@fujara] and simulations [@mount; @harrowell; @onuki]. Although there exist some theoretical attempts [@stilinger; @tarkiv; @liuopp; @bb; @xia], the underlying microscopic mechanism for the violation of the SE relation is not well understood. Recently, there have been many experimental and simulational studies of supercooled liquids that demonstrate the existence of kinetic heterogeneity which was often invoked to explain the origin of the non-exponential relaxation as well as the breakdown of the SE relation [@sillescu].

In relation to these questions on microscopic slow dynamic features in supercooled liquids, we deemed it worthwhile to investigate whether similar dynamic features can be found in simpler lattice spin systems or lattice gas systems. In this work, we show that the aforementioned features of 