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Prabodh Shukla

Publications and source records attributed to Prabodh Shukla.

30 records · Page 2Linked to original sources
arXiv2005

Voter Dynamics on an Ising Ladder: Coarsening and Persistence

Coarsening and persistence of Ising spins on a ladder is examined under voter dynamics. The density of domain walls decreases algebraically with time as $t^-{1/2}$ for sequential as well as parallel dynamics. The persistence probability decreases as $t^{-θ_{s}}$ under sequential dynamics, and as $t^{-θ_{p}}$ under parallel dynamics where $θ_{p} = 2 θ_{s} \approx .88$. Numerical values of the exponents are explained. The results are compared with the voter model on one and two dimensional lattices, as well as Ising model on a ladder under zero-temperature Glauber dynamics.

cond-mat.stat-mech↗
arXiv2004

Hysteresis in Ferromagnetic Random Field Ising Model with an Arbitrary Initial State

We present exact expressions for hysteresis loops in the ferromagnetic random field Ising model in the limit of zero temperature and zero driving frequency for an arbitrary initial state of the model on a Bethe lattice. This work extends earlier results that were restricted to an initial state with all spins pointing parallel to each other.

cond-mat.stat-mech↗
arXiv2004

Domains and Interfaces in Random Fields

We analyze the energetics of domains and interfaces in the presence of quenched random fields, particularly at the lower critical dimension of the random field Ising model. The relevance of this study to experiments is also discussed.

cond-mat.stat-mech↗
arXiv2004

Random Field Ising Model

Recent work on random field Ising model is described briefly emphasizing exact solutions of the model in simple cases and their relevance in understanding equilibrium and non-equilibrium properties of systems with quenched disorder.

cond-mat.stat-mech↗
arXiv2004

Driven Random Field Ising Model: some exactly solved examples in threshold activated kinetics

The random field Ising model driven by a slowly varying uniform external field at zero temperature provides a caricature of several threshold activated systems. In this model, the non-equilibrium response of the system can be obtained analytically on a Bethe lattice if the initial state of the system has all spins aligned parallel to each other. We consider ferromagnetic as well as anti-ferromagnetic interactions. The ferromagnetic model exhibits avalanches and non-equilibrium critical behavior. The anti-ferromagnetic model is marked by the absence of these features. The ferromagnetic model is Abelian, and the anti-ferromagnetic model is non-Abelian. Theoretical approaches based on the probabilistic method are discussed in the two cases, and illustrated by deriving some basic results.

cond-mat.stat-mech↗
arXiv2002

Hysteresis in the Random Field Ising Model and Bootstrap Percolation

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging $L^*$ increases as $exp(exp (J/Δ))$ in 2d, and as $exp(exp(exp(J/Δ)))$ in 3d, for disorder strength $Δ$ much less than the exchange coupling J. For system size $1 << L < L^*$, the coercive field $h_{coer}$ varies as $2J - Δ\ln \ln L$ for the square lattice, and as $2J - Δ\ln \ln \ln L$ on the cubic lattice. Its limiting value is 0 for L tending to infinity, both for square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and $h_{coer}$ tends to J.

cond-mat.stat-mech↗
arXiv2001

Distribution of Avalanche Sizes in the Hysteretic Response of Random Field Ising Model on a Bethe Lattice at Zero Temperature

We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of avalanche sizes s, as the external field increases from large negative to positive values. We solve these equations explicitly for a rectangular distribution of the random fields for a linear chain and the Bethe lattice of coordination number z=3, and show that in these cases, Prob(s) decreases exponentially with s for large s for all h on the hysteresis loop. We found that for z >3 and for small disorder, the magnetization shows a first order discontinuity for several continuous and unimodel distributions of random fields. The avalanche distribution Prob(s) varies as s^{-3/2} for large s near the discontinuity.

cond-mat.stat-mech↗
arXiv1999

Hysteresis in One-Dimensional Anti-Ferromagnetic Random-Field Ising Model at Zero-Temperature

We analyse hysteresis in a one-dimensional anti-ferromagnetic random field Ising model at zero-temperature. The random field is taken to have a rectangular distribution of width $2 Δ$ centered about the origin. A uniform applied field is varied slowly from $-\infty$ to $+\infty$ and back. Analytic expression for the hysteresis loop is obtained in the case $Δ\le |J|$, where $|J|$ is the strength of the nearest neighbor interaction.

cond-mat↗
arXiv1997

Zero-temperature Hysteresis in Random-field Ising Model on a Bethe Lattice

We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus infinity to plus infinity by setting up the self-consistent field equations, which we show are exact in this case. We find that for a 3-coordinated Bethe lattice, there is no jump discontinuity in magnetization for arbitrarily small gaussian disorder, but the discontinuity is present for larger coordination numbers. We have checked our results by Monte Carlo simulations employing a technique for simulating classical interacting systems on the Bethe lattice which avoids surface effects altogether.

cond-mat.stat-mech↗