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

Noise Predictions for STM in Systems with Local Electron Nematic Order

We propose that thermal noise in local stripe orientation should be readily detectable via STM on systems in which local stripe orientations are strongly affected by quenched disorder. Stripes, a unidirectional, nanoscale modulation of electronic charge, are strongly affected by quenched disorder in two-dimensional and quasi-two-dimensional systems. While stripe orientations tend to lock to major lattice directions, dopant disorder locally breaks rotational symmetry. In a host crystal with otherwise $C_4$ rotational symmetry, stripe orientations in the presence of quenched disorder map to the random field Ising model. While the low temperature state of such a system is generally a stripe glass in two dimensional or strongly layered systems, as the temperature is raised, stripe orientational fluctuations become more prevalent. We propose that these thermally excited fluctuations should be readily detectable in scanning tunneling spectroscopy as {\em telegraph noise} in the high voltage part of the local $I(V)$ curves. We predict the spatial, temporal, and thermal evolution of such noise, including the circumstances under which such noise is most likely to be observed. In addition, we propose an in-situ test, amenable to any local scanning probe, for assessing whether such noise is due to correlated fluctuations rather than independent switchers.Comment: 8 pages, 8 figure

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

Barkhausen noise in the Random Field Ising Magnet Nd2_2Fe14_{14}B

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field where thermal fluctuations dominate the dynamics.Comment: 16 pages, 7 figures. Under review at Phys. Rev.

Transverse Meissner Physics of Planar Superconductors with Columnar Pins

The statistical mechanics of thermally excited vortex lines with columnar defects can be mapped onto the physics of interacting quantum particles with quenched random disorder in one less dimension. The destruction of the Bose glass phase in Type II superconductors, when the external magnetic field is tilted sufficiently far from the column direction, is described by a poorly understood non-Hermitian quantum phase transition. We present here exact results for this transition in (1+1)-dimensions, obtained by mapping the problem in the hard core limit onto one-dimensional fermions described by a non-Hermitian tight binding model. Both site randomness and the relatively unexplored case of bond randomness are considered. Analysis near the mobility edge and near the band center in the latter case is facilitated by a real space renormalization group procedure used previously for Hermitian quantum problems with quenched randomness in one dimension.Comment: 23 pages, 22 figure

Space Representation of Stochastic Processes with Delay

We show that a time series $x_t$ evolving by a non-local update rule $x_t = f (x_{t-n},x_{t-k})$ with two different delays $k<n$ can be mapped onto a local process in two dimensions with special time-delayed boundary conditions provided that $n$ and $k$ are coprime. For certain stochastic update rules exhibiting a non-equilibrium phase transition this mapping implies that the critical behavior does not depend on the short delay $k$. In these cases, the autocorrelation function of the time series is related to the critical properties of directed percolation.Comment: 6 pages, 8 figure

Barkhausen Noise and Critical Scaling in the Demagnetization Curve

The demagnetization curve, or initial magnetization curve, is studied by examining the embedded Barkhausen noise using the non-equilibrium, zero temperature random-field Ising model. The demagnetization curve is found to reflect the critical point seen as the system's disorder is changed. Critical scaling is found for avalanche sizes and the size and number of spanning avalanches. The critical exponents are derived from those related to the saturation loop and subloops. Finally, the behavior in the presence of long range demagnetizing fields is discussed. Results are presented for simulations of up to one million spins.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.Comment: REVTEX, 10 pages including 4 figure