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Based on the fact that the underpotential electrochemical deposition of Agatoms on the $Au(100)$ surface exhibits sharp first-order phase transitions atwell-defined values of the (coexistence) chemical potential ($\mu_{coex}$), weperformed extensive simulations aimed at investigating the hysteretic dynamicbehavior of the system close to coexistence upon the application of a periodicsignal of the form $\mu(t) = \mu_{coex} + \mu_{o}sin(2\Pi t/\tau) $, where$\mu_{o}$ and $\tau$ are the amplitude and the period of the sweep,respectively. For relatively short periods and small enough amplitudes thesystem becomes trapped either at low or high Ag coverage states, as evidencedby recording hysteresis loops. This scenario is identified as dynamicallyordered states (DOS), such that the relaxation time $(\tau_{relax})$ of thecorresponding metastable state obeys $\tau_{relax} > \tau $. On the other hand,by properly increasing $\mu_{o}$ or/and $\tau$, one finds that the $Ag$coverage gently follows the external drive (here $\tau_{relax} < \tau $) andthe system is said to enter into dynamically disordered states (DDS), wherehysteresis loops show almost symmetric limiting cycles. This symmetry breakingbetween limiting cycles driven by an external signal is discussed in terms ofthe concept of (out-of-equilibrium) Dynamic Phase Transitions between DOS andDDS, similar to those encountered when a magnetic system is placed in thepresence of a variable external magnetic field. However, a careful finite-sizescaling study reveals that, at least at $T = 300K$, the $Ag/Au(100)$ systemdoes not exhibit true second-order phase transitions but rather a crossoverbehavior between states. A diagram showing the location of the ordered anddisordered states in the $\mu$ versus $\tau$ plane is obtained and discussed.

Dynamic response of Ag monolayers adsorbed on Au(100) upon an oscillatory variation of the chemical potential: A Monte Carlo simulation study