Rayleigh loops in the random-field Ising model on the Bethe lattice

Colaiori, Francesca; Gabrielli, Andrea; Zapperi, Stefano

doi:10.1103/physrevb.65.224404

Cited by 14 publications

(34 citation statements)

References 23 publications

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“…Thus, there is an intermediate region where the GS is ferromagnetic but the DS is paramagnetic. To further corroborate our findings, we analyze the RFIM on the Bethe lattice: We compute the GS magnetization and compare it with the remanent magnetization of the DS [19]. While the exponents are the same in the two cases (coinciding with mean-field results), the Bethe lattice reproduces the ordering of the critical points in d 3.…”

Section: Phase Transitions In a Disordered System In And Out Of Equilsupporting

confidence: 52%

“…1 To provide another viewpoint and corroborate our claims, we compare the GS and DS on the Bethe lattice where analytical expressions can be found exactly. The RFIM displays also on the Bethe lattice, for a large enough coordination number z, both an equilibrium and a nonequilibrium disorder-induced phase transition [19]. To compare the GS and the DS around the respective transitions, we take directly the thermodynamic limit, using for the DS the results of Ref.…”

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

“…. [19] and R GS c ' 1:8375, with the mean-field exponent ( 1=2). When plotted against R ÿ R c =R c , the two curves superimpose close to the critical point.…”

Section: We Collapse the P H Y S I C A L R E V I E W L E T T E R Smentioning

confidence: 99%

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Phase Transitions in a Disordered System in and out of Equilibrium

et al. 2004

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The equilibrium and non-equilibrium disorder induced phase transitions are compared in the random-field Ising model (RFIM). We identify in the demagnetized state (DS) the correct nonequilibrium hysteretic counterpart of the T = 0 ground state (GS), and present evidence of universality. Numerical simulations in d = 3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.

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Section: Phase Transitions In a Disordered System In And Out Of Equilsupporting

confidence: 52%

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

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Phase Transitions in a Disordered System in and out of Equilibrium

et al. 2004

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“…However, a formal physical description of the origin of the experimentally observed behavior has been, to date, lacking. As Rayleigh behavior is ubiquitous, 16,17 these results are relevant not only for purely ferroelectric but also for ferroelastic, ferromagnetic, and multiferroic materials.…”

Section: Introductionmentioning

confidence: 96%

Strain-modulated piezoelectric and electrostrictive nonlinearity in ferroelectric thin films without active ferroelastic domain walls

Bassiri‐Gharb

Trolier-McKinstry

Damjanović

2011

Journal of Applied Physics

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High-temperature piezoresponse force microscopy Appl. Phys. Lett. 99, 173103 (2011) Comparison of structural and electric properties of PbZr0.2Ti0.8O3 and CoFe2O4/PbZr0.2Ti0.8O3 films on (100)LaAlO3 J. Appl. Phys. 110, 064115 (2011) Influence of Mn doping on domain wall motion in Pb(Zr0.52Ti0.48)O3 films J. Appl. Phys. 109, 064105 (2011) Critical thickness for extrinsic contributions to the dielectric and piezoelectric response in lead zirconate titanate ultrathin films J. Appl. Phys. 109, 014115 (2011) Enhanced critical temperature in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films on silicon Appl. Phys. Lett. 98, 012903 (2011) Additional information on J. Appl. Phys. In contrast to usual assumptions, it is shown that even when ferroelastic domain walls are inactive or absent, the motion of ferroelectrically active interfaces in ferroelectric materials contributes, at subcoercive electric fields, not only to the polarization but also to the strain. Specifically, in polycrystalline samples, strain coupling between adjacent grains, or mediated through the substrate in thin films, influences both the dielectric and piezoelectric response. The model developed explains the unexpected observation of piezoelectric nonlinearity in films even in cases in which the domain variants' projections are equivalent along the direction of the external driving field.

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“…Is the entropy density (associated with the number of metastable states) positive everywhere ? The situation is especially intriguing in the low-disorder regime where a region around the origin becomes inaccessible to any field history that starts from the saturated states [12]. The aim of this work is thus to calculate the number of metastable configurations with a fixed magnetization m per spin as a function of the external field H. We consider a Gaussian distribution of the random fields whose width R measures the "strength" of the disorder, and, in order to analyze the problem analytically (at least partially), we work on a Bethe lattice defined here as a random graph of fixed connectivity z [13], i.e.…”

Section: Introductionmentioning

confidence: 99%

Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

2005

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We study the ferromagnetic random-field Ising model on random graphs of fixed connectivity z (Bethe lattice) in the presence of an external magnetic field H. We compute the number of singlespin-flip stable configurations with a given magnetization m and study the connection between the distribution of these metastable states in the H − m plane (focusing on the region where the number is exponentially large) and the shape of the saturation hysteresis loop obtained by cycling the field between −∞ and +∞ at T = 0. The annealed complexity ΣA(m, H) is calculated for z = 2, 3, 4 and the quenched complexity ΣQ(m, H) for z = 2. We prove explicitly for z = 2 that the contour ΣQ(m, H) = 0 coincides with the saturation loop. On the other hand, we show that ΣA(m, H) is irrelevant for describing, even qualitatively, the observable hysteresis properties of the system.

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Rayleigh loops in the random-field Ising model on the Bethe lattice

Cited by 14 publications

References 23 publications

Phase Transitions in a Disordered System in and out of Equilibrium

Phase Transitions in a Disordered System in and out of Equilibrium

Strain-modulated piezoelectric and electrostrictive nonlinearity in ferroelectric thin films without active ferroelastic domain walls

Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

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