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Dynamical quantum phase transitions (DQPTs) feature singular temporalbehavior in transient quantum states during nonequilibrium real-time evolution.In this work we show that DQPTs in random Ising chains exhibit criticalbehavior with nontrivial exponents that are not integer valued and not ofmean-field type. By means of an exact renormalization group transformation weestimate the exponents with high accuracy eliminating largely any finite-sizeeffects. We further discuss how the considered dynamical phenomena can be madeaccessible in current Rydberg atom platforms. In this context we exploresignatures of the DQPTs in the statistics of spin configuration measurementsavailable in such architectures. Specifically, we study the statistics ofclusters of consecutively aligned spins and observe a marked influence of theDQPT on the corresponding distribution.

Unconventional critical exponents at dynamical quantum phase transitions in a random Ising chain