Hysteresis in the antiferromagnetic random-field Ising model at zero temperature

Kurbah, Lobisor; Shukla, Prabodh

doi:10.1103/physreve.83.061136

Cited by 5 publications

(3 citation statements)

References 42 publications

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“…We next considered a model of Ising spins interacting via a long-range antiferromagnetic coupling, which is expected to display a non-zero θ [26]. Our analysis is relevant, since models with antiferromagnetic interactions are seldom studied [30,31] in relation to the avalanches that occur during a hysteresis loop. We investigated this model using numerical simulations and analysed the features of the gap distribution.…”

Section: Discussionmentioning

confidence: 99%

Gaps between avalanches in one-dimensional random-field Ising models

et al. 2017

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We analyze the statistics of gaps (ΔH) between successive avalanches in one-dimensional random-field Ising models (RFIMs) in an external field H at zero temperature. In the first part of the paper we study the nearest-neighbor ferromagnetic RFIM. We map the sequence of avalanches in this system to a nonhomogeneous Poisson process with an H-dependent rate ρ(H). We use this to analytically compute the distribution of gaps P(ΔH) between avalanches as the field is increased monotonically from -∞ to +∞. We show that P(ΔH) tends to a constant C(R) as ΔH→0^{+}, which displays a nontrivial behavior with the strength of disorder R. We verify our predictions with numerical simulations. In the second part of the paper, motivated by avalanche gap distributions in driven disordered amorphous solids, we study a long-range antiferromagnetic RFIM. This model displays a gapped behavior P(ΔH)=0 up to a system size dependent offset value ΔH_{off}, and P(ΔH)∼(ΔH-ΔH_{off})^{θ} as ΔH→H_{off}^{+}. We perform numerical simulations on this model and determine θ≈0.95(5). We also discuss mechanisms which would lead to a nonzero exponent θ for general spin models with quenched random fields.

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Section: Discussionmentioning

confidence: 99%

Gaps between avalanches in one-dimensional random-field Ising models

et al. 2017

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“…In the equilibrium case, d l =1 for the Ising model, and d l =2 for the randomfield Ising model [6][7][8]. For the 2d ferromagnetic Ising model solved by Onsager [9] on a square lattice, the existence of a critical point is not supposed to depend on whether the lattice is square, triangular 1 , or honeycomb [10]. The short range structure of the lattice is irrelevant under a diverging correlation length.…”

Section: Introductionmentioning

confidence: 99%

Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number

Shukla¹,

Thongjaomayum²

2016

J. Phys. A: Math. Theor.

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We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1 − c have z = 3. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of c > 0. This extends earlier results for c = 0 and c = 1 to the entire range 0 ≤ c ≤ 1, and provides new insight in non-equilibrium critical phenomena.

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“…Hysteresis in RFIM with asymmetric distribution of quenched random fields in the limit of low disorder was studied [6] and the spin flip was found to be related to bootstrap percolation. Athermal hysteresis was also studied [7] in antiferromagnetic RFIM recently. The statistics [8] and the dynamical critical behaviour of avalanches [9] was studied in RFIM.…”

Section: Introductionmentioning

confidence: 99%

Standing spin wave mode in RFIM: Patterns and athermal nonequilibrium phases

Acharyya

2015

Journal of Magnetism and Magnetic Materials

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The dynamical responses of random field Ising model at zero temperature, driven by standing magnetic field wave, is studied by Monte Carlo simulation in two dimensions. The three different kinds of distribution of quenched random field are used here, uniform, bimodal and Gaussian. In all cases, three distinct dynamical phases were observed, namely, the pinned, structured and random. In the pinned phase no spin flip is observed. In the structured phase standing spin wave modes are observed. The random phase is shown with no observed regular pattern. For a fixed value of the amplitude of the standing magnetic field wave, in the region of small quenched field, the system remains in a pinned phase. In the intermediate range of values of random field, a standing spin wave mode (structured phase) is observed. The regular pattern of this spin wave mode disappears for higher values of random field yielding a random phase. The comprehensive phase baundaries are drawn in all three cases. The boundary of pinned phase are analytically calculated for uniform and bimodal types of quenched random fields.Keywords: RFIM, Standing wave, Quenched random field, Monte Carlo simulationThe random field Ising model (RFIM) is a simple model to understand various physical phenomena, like, hysteresis[1], Barkhausen noise [2] observed in ferromagnetic materials, avalanche [3], return point memory effects etc. The RFIM was studied theoretically with intense attention. RFIM was solved exactly[4] on Bethe lattice and the qualitative behaviour of magnetisation as a function of external magnetic field was found to depend on the coordination number of Bethe lattice. The effect of coordination number on the nonequilibrium critical point in RFIM was studied [5] in details. Hysteresis in RFIM with asymmetric distribution of quenched random fields in the limit of low disorder was studied[6] and the spin flip was found to be related to bootstrap percolation. Athermal hysteresis was also studied [7] in antiferromagnetic RFIM recently. The statistics [8] and the dynamical critical behaviour of avalanches [9] was studied in RFIM. All these studies mentioned here are static in a sense that the time dependence of any quantity is studied.The dynamical behaviours of the driven RFIM are also quite interesting. The RFIM has also served to study the dynamics of domain wall. The motion of domain wall by magnetic field in a 2D ultrathin Pt/Co/Pt film (showing perpendicular anisotropy and quenched disorder which is analogous to RFIM) was studied [10] experimentally by magneto optical polar Kerr imagning technique. The motion of moving interface was analyzed numerically [11] in the RFIM driven by external magnetic field. Later, the depinning transition of driven interface was studied [12]. The creep motion of interface in driven RFIM was studied [13] and the nonlinear field-velocity relationship was found.All the studies mentioned above have a very common feature. Firstly, the external driving magnetic field was varied is a quasi-static manner. Secondly,...

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Hysteresis in the antiferromagnetic random-field Ising model at zero temperature

Cited by 5 publications

References 42 publications

Gaps between avalanches in one-dimensional random-field Ising models

Gaps between avalanches in one-dimensional random-field Ising models

Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number

Standing spin wave mode in RFIM: Patterns and athermal nonequilibrium phases

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