Universality in models for disorder-induced phase transitions

Vives, Eduard; Goicoechea, J.; Ortı́n, Jordi; Planes, Antoni

doi:10.1103/physreve.52.r5

Cited by 62 publications

(59 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The agreement is very satisfactory confirming universality. 6,33 Table I also includes the values of the exponents corresponding to mean-field calculations. Clearly, when considering the full set of all the critical exponents, one concludes that the mean-field model does not belong to the same universality class.…”

Section: Discussionmentioning

confidence: 99%

Hysteresis and avalanches in the random anisotropy Ising model

Vives

Planes

2001

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

The behavior of the random anisotropy Ising model at Tϭ0 under local relaxation dynamics is studied. The model includes a dominant short-range ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. As a consequence, some of the effective interactions become antiferromagneticlike and frustration appears. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occurring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump ͑large avalanche spanning a macroscopic fraction of the system͒ to a rather smooth loop exhibiting only tiny avalanches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.

show abstract

Section: Discussionmentioning

confidence: 99%

Hysteresis and avalanches in the random anisotropy Ising model

Vives

Planes

2001

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…We model this by the zero-temperature, single-spin flips, energy minimizing dynamics of the energy function ( Fig. 1) [19][20][21]:…”

Section: B Mapping To a Spin-1 Ising Modelmentioning

confidence: 99%

Shear-induced rigidity in athermal materials: A unified statistical framework

Sarkar

Chakraborty

2015

Phys. Rev. E

View full text Add to dashboard Cite

Recent studies of athermal systems such as dry grains and dense, non-Brownian suspensions have shown that shear can lead to solidification through the process of shear jamming in grains and discontinuous shear thickening in suspensions. The similarities observed between these two distinct phenomena suggest that the physical processes leading to shear-induced rigidity in athermal materials are universal. We present a non-equilibrium statistical mechanics model, which exhibits the phenomenology of these shear-driven transitions: shear jamming and discontinuous shear thickening in different regions of the predicted phase diagram. Our analysis identifies the crucial physical processes underlying shear-driven rigidity transitions, and clarifies the distinct roles played by shearing forces and the density of grains.

show abstract

“…[34,40] A remarkable aspect of longrange interacting glasses is the fact that the distribution of avalanche sizes is scale free all along the hysteresis loop [14], in contrast to what one finds in many ferromagnetic model systems, such as the random field Ising model, where such criticality requires fine-tuning, both of the disorder strength and the externally applied field. [41,42] A. Distribution of local fields in mean-field spin glasses…”

Section: Spin Glassesmentioning

confidence: 99%

Marginal Stability in Structural, Spin, and Electron Glasses

Müller

Wyart

2015

Annu. Rev. Condens. Matter Phys.

180

264

View full text Add to dashboard Cite

We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the distribution of local fields and crackling in systems with long-range interactions. We show how the principle of marginal stability offers a unifying perspective on the phenomenology of systems as diverse as spin and electron glasses, hard spheres, pinned elastic interfaces and the plasticity of soft amorphous solids.

show abstract

Universality in models for disorder-induced phase transitions

Cited by 62 publications

References 13 publications

Hysteresis and avalanches in the random anisotropy Ising model

Hysteresis and avalanches in the random anisotropy Ising model

Shear-induced rigidity in athermal materials: A unified statistical framework

Marginal Stability in Structural, Spin, and Electron Glasses

Contact Info

Product

Resources

About