supercooled liquids, [*i.e.*]{}, slowing-down, non-exponential relaxation and the (analogue) of the breakdown of the SE relation, are also observed in a two-dimensional (2D) lattice Coulomb gas (LCG) system. We also find that the relaxation of the system exhibits a spontaneous appearance of spatial heterogeneity, which we argue is the underlying cause for the non-exponential relaxation and the breakdown of the SE relation.

In recent years, there have been some efforts to find glassy dynamic features in the lattice spin systems with nonrandom interactions [@bulbul]. One of the well-known examples of disorder-free lattice model system is uniformly frustrated XY (UFXY) models in two dimensions, which serve as a model for two dimensional arrays of Josephson junctions under the influence of uniform transverse magnetic fields. Recent work [@kl] has shown that, irrespective of the true nature of the low temperature phase of this system, the equilibrium dynamics of UFXY model in the intermediate range of the temperature for frustration parameter $f$ near $1-g \equiv (3-\sqrt{5})/2 \simeq 0.382$, exhibits a close analogy to that of supercooled liquids. Both spin and vortex dynamics show stretched exponential relaxations with temperature dependent stretched exponents. In order to investigate the dynamics of this system in more detail, 