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

TL;DR

This paper investigates how violations of the no-passing property in a frustrated disordered spin model lead to a discontinuity in the distribution of field increments between avalanches, revealing a new dynamical signature of frustration.

Contribution

It demonstrates that in the RFBEGM, breaking the no-passing property combined with frustration causes a distinct discontinuity in avalanche field increments, supported by analytical and numerical evidence.

Findings

Discontinuity appears in the distribution of avalanche triggering fields.

Violation of no-passing combined with frustration induces blocking effects.

Analytical predictions match numerical simulations for the discontinuity onset.

Abstract

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.