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Abstract

We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations demonstrate that in the strongly interacting regime, the system exhibits a distinct set of universal critical exponents, markedly different from those observed in the weakly interacting limit. This dichotomy aligns with experimental findings on the metal-insulator transition in 2DEGs, where high interaction strength (low carrier density) leads to qualitatively different behavior. The analysis includes scaling of the average electron density with temperature, the power spectral density, and the statistics of electronic avalanches - namely their size distributions and autocorrelation functions. In all cases, the extracted exponents differ significantly between the weak and strong interaction regimes, highlighting the emergence of two universality classes governed by interaction strength. These results underscore the critical role of electron correlations in the self-organized behavior of low-dimensional electronic systems.