Discontinuity in the distribution of field increments between avalanches in the non-Abelian random field Blume-Emery-Griffiths model with no passing violation

We study the zero-temperature quasi-statically driven dynamics of the random field Blume--Emery--Griffiths model (RFBEGM) as a minimal framework to investigate the consequences of violating the no-passing property in driven disordered systems. While the random field Ising model obeys no-passing and displays abelian relaxation dynamics, we show that this property is generically violated in the RFBEGM. By systematically exploring the full parameter space of the fully connected model, we identify the regimes in which no-passing is broken and demonstrate that, when this violation is combined with frustration induced by a repulsive biquadratic coupling, it leaves a clear dynamical signature. Specifically, the distribution of the minimal field increment required to trigger successive avalanches develops a discontinuity that is absent both in no-passing dynamics and in unfrustrated no-passing-violating regimes. We provide analytical arguments that locate the onset of this discontinuity, in excellent agreement with numerical simulations. Our results establish this discontinuity as a robust diagnostic of frustration-induced blocking in non-abelian avalanche dynamics within a mean-field setting, without making claims about new universality classes.