Random Field Ising Model In and Out of Equilibrium

We present numerical studies of zero-temperature Gaussian random-field Ising model (zt-GRFIM) in both equilibrium and non-equilibrium. We compare the no-passing rule, mean-field exponents and universal quantities in 3D (avalanche critical exponents, fractal dimensions, scaling functions and anisotropy measures) for the equilibrium and non-equilibrium disorder-induced phase transitions. We show compelling evidence that the two transitions belong to the same universality class.Comment: 4 pages, 2 figures. submitted to Phys. Rev. Let

No-passing Rule in the Ground State Evolution of the Random-Field Ising Model

We exactly prove the no-passing rule in the ground state evolution of the random-field Ising model (RFIM) with monotonically varying external field. In particular, we show that the application of the no-passing rule can speed up the calculation of the zero-temperature equilibrium $M(H)$ curve dramatically.Comment: 7 pages, 4 figure

Transforming mesoscale granular plasticity through particle shape

When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are imaged with x-rays. We introduce volatility, a quantity from economic theory, as a powerful new tool to quantify the magnitude of stress fluctuations, finding systematic, shape-dependent trends. For all 22 investigated shapes the magnitude $s$ of relaxation events is well-fit by a truncated power law distribution $P(s)\sim {s}^{-\tau} exp(-s/s^*)$, as has been proposed within the context of plasticity models. The power law exponent $\tau$ for all shapes tested clusters around $\tau=$ 1.5, within experimental uncertainty covering the range 1.3 - 1.7. The shape independence of $\tau$ and its compatibility with mean field models indicate that the granularity of the system, but not particle shape, modifies the stress redistribution after a slip event away from that of continuum elasticity. Meanwhile, the characteristic maximum event size $s^*$ changes by two orders of magnitude and tracks the shape dependence of volatility. Particle shape in granular materials is therefore a powerful new factor influencing the distance at which an amorphous system operates from scale-free criticality. These experimental results are not captured by current models and suggest a need to reexamine the mechanisms driving mesoscale plastic deformation in amorphous systems.Comment: 11 pages, 8 figures. v3 adds a new appendix and figure about event rates and changes several parts the tex

Hysteresis and Noise from Electronic Nematicity in High Temperature Superconductors

An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using noise and hysteresis. In particular, we have uncovered a remarkably robust linear relation between the orientational order and the resistance anisotropy which holds over a wide range of circumstances.Comment: References added; minor wording change