A theory, based on the Landau-Ginzburg formalism, shows that remarkabl
e singularities in currents of electrode charge transfer reactions occ
ur near the critical potentials where second-order surface phase trans
itions take place. This happens if the fluctuations of the order param
eter, which describes the transition, are exponentially coupled to the
reaction system via fluctuating tunneling or activation barriers. Cou
pling depending on the sign of the order parameter is considered; the
corresponding singularities in Arrhenius and Tafel plots for electrode
currents are predicted, and the perspectives for their experimental i
nvestigation are discussed.