We numerically investigate heating-and-cooling quenches taking place entirely in the nonordered phase of the discrete Gross-Pitaevskii equation on a three-dimensional cubic lattice. In equilibrium, this system exhibits a $U\left(1\right)$-ordering phase transition at an energy density which is significantly lower than the minimum one during the quench. Yet, we observe that the postquench relaxation is accompanied by a transient $U\left(1\right)$ ordering, namely, the correlation length of $U\left(1\right)$ fluctuations significantly exceeds its equilibrium prequench value. The longer and the stronger the heating stage of the quench, the stronger is the $U\left(1\right)$ transient ordering. We identify the origin of this ordering with the emergence of a small group of slowly relaxing lattice sites accumulating a large fraction of the total energy of the system. Our findings suggest that the transient ordering may be a robust feature of a broad class of physical systems. This premise is consistent with the growing experimental evidence of the transient $U\left(1\right)$ order in rather dissimilar settings.

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• Dynamical phase transitions
• Nonequilibrium statistical mechanics
• Quantum quench
• Nonequilibrium lattice models
• Nonequilibrium systems