Avalanche distributions in the two-dimensional nonequilibrium zero-temperature random field Ising model

Spasojević, Djordje; Janićević, Sanja; Knežević, Milan

doi:10.1103/physreve.84.051119

Cited by 45 publications

(36 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equilibrium RFIM has been shown to have a LCD equal to two [17], and the same is believed to be true for the front-propagation variant of the NE-RFIM [18]. For the nucleated model we study here, some suggest that the LCD is two [19,20], others suggest that power-laws are indeed able to capture the behavior and no crossover occurs in 2D [21,22], and some suggest that a lower critical dimension does not exist for this model [23][24][25][26]. Here, we derive the expected non-power-law scaling in the LCD from a nonlinear renormalization-group analysis, and find excellent agreement with the data presuming an LCD of two, while power-law scaling fails to capture the behavior.• Is the value of the critical disorder in D = 2 zero, or positive?…”

supporting

confidence: 53%

“…This behavior in conjunction with the observation that for both the equilibrium and front-propagation problems, r c is found arXiv:1906.10568v2 [cond-mat.dis-nn] 13 Aug 2019 to be zero [18] suggests that r c may be quite small. Early work on the nucleated model, presuming power law scaling [20,28,29], yielded positive r c = 0.75 ± 0.03 [28], but more recent work on larger systems finds a smaller r c = 0.54 ± 0.02 [21,22] collapsing over a small range r ∈ [0.64, 0.70]. Our non-power-law scaling form would predict that power-law fits at a given system size should succeed in small ranges of disorder, but that larger system sizes will yield lower and lower predicted critical disorders.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Unusual scaling for two-dimensional avalanches: Curing the faceting and scaling in the lower critical dimension

Hayden

Raju

Sethna

2019

Phys. Rev. Research

View full text Add to dashboard Cite

The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the invariant arguments of the universal scaling functions necessary to perform scaling collapses can be directly determined using our recent normal form theory of the Renormalization Group. This method has proven useful in cleanly capturing the complex behavior which occurs in both the lower and upper critical dimensions of systems and here captures the 2D NE-RFIM behavior well. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of 10 4 in avalanche cutoff. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.We study the avalanche size distribution in the two-dimensional nucleated non-equilibrium random-field Ising model (NE-RFIM), simulated on a Voronoi lattice to bypass faceting, and analyzed using the scaling predictions of the nonlinear renormalization-group flows predicted for the lower critical dimension. We find excellent agreement over a large critical region, addressing several outstanding issues in the field.The NE-RFIM is perhaps the best-understood model of crackling noise [1], exhibiting power-law distributions of avalanche sizes at a critical disorder r c representing the standard deviation of the strength of the random field at each site. The model transitions from a 'downspin' state to an 'up-spin' state as an external field H increases. Above the critical disorder r c , this transition is composed of avalanches of spins of size limited by a typical cutoff Σ + (r); below the critical disorder a finite fraction of the spins flip in a single event, with precursors and aftershock sizes limited by Σ − (r). This model, albeit simple, contains the necessary ingredients to describe hysteretic and avalanche behaviors in a diverse set of systems. Barkhausen noise in magnets [2] decision making in socio-economics [3], absorption and desorption in superfluids [4,5] as well as the effects of nematicity in high T c superconductors [6-8] can each be understood in terms of 'crackling noise' naturally described by the NE-RFIM.Although the NE-RFIM itself has been around in various forms since the 1970s [9], there are still a number of current questions and issues:• Is it in the same universality class as the equilibrium RFIM model [10]? It has long been debated whether the equilibrium and non-equilibrium versions of the model are in the same universality class. This question of universality has been approached in a number of ways which have suggested the same class for the two models [11][12][13][14][15][16]. Recent wor...

show abstract

supporting

confidence: 53%

mentioning

confidence: 99%

Unusual scaling for two-dimensional avalanches: Curing the faceting and scaling in the lower critical dimension

Hayden

Raju

Sethna

2019

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…Disordered ferromagnetic films exhibiting criticality at the hysteresis loop [4,11,[16][17][18] are conveniently modeled by two-dimensional random-field Ising model (2D-RFIM) [19][20][21], as described in Section II. Besides, these model systems are also of high importance for theoretical considerations for the following reasons.…”

Section: Introductionmentioning

confidence: 99%

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

Tadić

2018

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length L x is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance L y . By fixing the number of spins N = L x × L y = 10 6 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range L x /L y ∈ [1/16, 16]. The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter L x and height L y . We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios L x /L y . The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

show abstract

“…4, and critical exponents obtained through this analysis are given in Table I these are in good agreement with the corresponding exponents obtained through the scaling relations (within statistical error). The collapsing width for the various curves was also calculated [41]. Although in the present study the network is externally driven to criticality by varying the control parameter λ, avalanches showing power-law behaviour also form an integral part of the study of self-organized critical neuronal systems [10].…”

Section: Avalanche Propertiesmentioning

confidence: 93%

“…(15)(16)(17). We study networks with degree K = 4 and system size N = 1024 2 at the critical point (for µ = 1) and compute joint distributions [41,42] for four pairs of the above related quantities, size-duration (see Fig. 3) as well as size-magnitude, size-area and size-energy (which are not shown here).…”

Section: Avalanche Propertiesmentioning

confidence: 99%

Scaling behavior in probabilistic neuronal cellular automata

2013

View full text Add to dashboard Cite

We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.

show abstract

Avalanche distributions in the two-dimensional nonequilibrium zero-temperature random field Ising model

Cited by 45 publications

References 26 publications

Unusual scaling for two-dimensional avalanches: Curing the faceting and scaling in the lower critical dimension

Unusual scaling for two-dimensional avalanches: Curing the faceting and scaling in the lower critical dimension

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

Scaling behavior in probabilistic neuronal cellular automata

Contact Info

Product

Resources

About