Geometry-induced non-equilibrium phase transition in sandpiles

Abstract

We study the sandpile model on three-dimensional spanning Ising clusters with the temperature $T$ treated as the control parameter. By analyzing the three dimensional avalanches and their two-dimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOC${}_{T=\infty }$), along with a tricritical point (at $T_c$, the critical temperature of the host) between them. The transition between these two criticalities is induced by the transition in the support. The SOC${}_{T=\infty }$ universality class is characterized by the exponent of the avalanche size distribution ${\tau }^{T=\infty }=1.27\pm 0.03$, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets (Phys. Rev. L 84, 4705 (2000)). The tricritical point is characterized by its own critical exponents. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP) and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of $\epsilon \equiv \frac{T-T_c}{T_c}$, defining further critical exponents. Importantly the finite size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents $\beta =0.19\pm 0.02$ and $\nu =0.75\pm 0.05$. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against $T$ with the numerical value $D_f=1.25\pm 0.01$.

References in corpus (14)

• Avalanches, Barkhausen Noise, and Plain Old Criticality
• Self-Organized Criticality model for Brain Plasticity
• Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets
• Experiments in vortex avalanches
• The universality class of absorbing phase transitions with a conserved field
• The Magnetization of the 3D Ising Model
• Dynamics of a ferromagnetic domain wall and the Barkhausen effect
• Universal Pulse Shape Scaling Function and Exponents: A Critical Test for Avalanche Models applied to Barkhausen Noise
• Modelling Financial Markets by Self-Organized Criticality
• The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension
• Critical bursts in filtration
• Modelling the influence of photospheric turbulence on solar flare statistics
• Statistical Investigation of Avalanches of Three Dimensional Small-World Networks and their Boundary and Bulk Cross-Sections
• Sandpile on uncorrelated site-diluted percolation lattice; From three to two dimensions

Cited by in corpus (5)

• Two temperature Ising Model
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• Response of the competitive balance model to the external field
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