Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet

Griffiths, Robert B.

doi:10.1103/physrevlett.23.17

Cited by 1,536 publications

(1,134 citation statements)

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“…2 and 3), attributed to the onset of the GL phase. 26 The fact that the anomaly appears simultaneously in χ and χ indicates that the onset of the GL phase is accompanied by an energy dissipation process. The fit of the inverse of χ to a Curie-Weiss law ( Fig.…”

Section: Resultsmentioning

confidence: 99%

Griffiths-like phase and magnetic correlations at high fields in Gd5Ge4

et al. 2011

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Magnetic correlations appearing in polycrystalline Gd 5 Ge 4 are studied. On the one hand, ac susceptibility measurements as functions of temperature at several dc fields and frequencies show the existence of ferromagnetic (FM) and antiferromagnetic (AFM) correlations in the paramagnetic (PM) region, where a Griffiths-like phase appears below ∼225 K. The value for the effective magnetic moment within the Griffiths-like phase is 10.1 μ B . FM correlations also extended all the way into the AFM phase below ∼127 K. The onset of the Griffiths-like phase is associated with an effective critical slowing down. On the other hand, high field magnetization measurements reveal the presence of FM and AFM correlations in the three magnetic phases (PM, FM, and AFM), giving rise to a variety of mixed magnetic states. In particular, at high fields the magnetostructural transition takes place in several stages that extend along a wide temperature range. A three-dimensional (T ,H,M) phase diagram is proposed, including the new experimental findings.

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Section: Resultsmentioning

confidence: 99%

Griffiths-like phase and magnetic correlations at high fields in Gd5Ge4

et al. 2011

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“…(13) and (21). For β < 1 localization takes certainly place if the lower bound on the Ruelle pressure is larger than the mean field value, i.e.,…”

Section: The Delocalization Regionmentioning

confidence: 99%

Thermodynamic formalism and localization in Lorentz gases and hopping models

et al. 1997

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The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure ψ(β). The inversetemperature like variable β allows one to scan the structure of the probability distribution in the dynamic phase space. This formalism is applied here to a Lorentz Lattice Gas, where a particle moving on a lattice of size L d collides with fixed scatterers placed at random locations. Here we give rigorous arguments that the Ruelle pressure in the limit of infinite systems has two branches joining with a slope discontinuity at β = 1. The low and high β-branches correspond to localization of trajectories on respectively the "most chaotic" (highest density) region, and the "most deterministic" (lowest density) region, i.e. ψ(β) is completely controlled by rare fluctuations in the distribution of scatterers on the lattice, and it does not carry any information on the global structure of the static disorder.As β approaches unity from either side, a localization-delocalization transition leads to a state where trajectories are extended and carry information on transport properties. At finite L the narrow region around β = 1 where the trajectories are extended scales as (ln L) −α , where α depends on the sign of 1 − β, if d > 1, and as (L ln L) −1 if d = 1. This result appears to be general for diffusive systems with static disorder, such as random walks in random environments or for 1 permanent address: CNRS, LPS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 PARIS Cedex 05, France 1 the continuous Lorentz gas. Other models of random walks on disordered lattices, showing the same phenomenon, are discussed.

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“…The presence of thermodynamic and dynamic singularities due to rare regions in systems with quenched randomness and a phase transition was first pointed out by Griffiths [52] and by McCoy [53]. We will follow current usage and call these effects "Griffiths effects".…”

Section: Introductionmentioning

confidence: 99%

“…They are one type of precursor to the phase transition: rare, large but finite "inclusions" of the other phase, i.e., regions in which (because of highly atypical configurations of the quenched randomness) the parameters of the system are locally such that it appears to be in the other phase. Such Griffiths effects have been studied extensively at conventional thermal [52,53] and quantum phase transitions [54,55]; see e.g. Ref.…”

Section: Introductionmentioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

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Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet

Abstract: It is shown that in a class of randomly diluted Ising ferromagnets the magnetization fails to be an analytic function of the field H at H= 0 for a range of temperatures above that at which spontaneous magnetization first appears.

Cited by 1,536 publications

References 10 publications

Griffiths-like phase and magnetic correlations at high fields in Gd5Ge4

Griffiths-like phase and magnetic correlations at high fields in Gd5Ge4

Thermodynamic formalism and localization in Lorentz gases and hopping models

Rare‐region effects and dynamics near the many‐body localization transition

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