Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

Sharma, Rati; Cherayil, Binny J.

doi:10.1103/physreve.81.021804

Cited by 23 publications

(22 citation statements)

References 24 publications

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“…For Ising SGs in a random magnetic field of mean zero and standard deviation h, the same (extended) BR action can be derived. In addition, for a SG in which the spins are m-component unit vectors, inclusion of a mean zero, isotropically-distributed vector-valued random field of standard deviation h also produces an AT line within mean-field theory [33]. The same BR action applies there, so that similar results are predicted for low-dimensional XY and Heisenberg SGs in a random magnetic field.…”

Section: B Outline and Resultssupporting

confidence: 55%

One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses

Höller

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2020

Phys. Rev. E

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The de Almeida-Thouless (AT) line is the phase boundary in the temperature-magnetic field plane of an Ising spin glass at which a continuous (i.e. second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension d, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: a) for d − 6 small and positive, with increasing field on the AT line first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as d → 6 + ; b) for d ≤ 6, we argue that the quasi-first-order transition persists down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in simulations and high-temperature series expansions. arXiv:1909.03284v2 [cond-mat.stat-mech]

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Section: B Outline and Resultssupporting

confidence: 55%

One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses

Höller

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2020

Phys. Rev. E

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“…There is, as yet, no analytically soluble but non-trivial random-field model, analogous to that of the SK model for frustrated exchange disorder [101]. When there are random fields in addition to SK-like random bond disorder a sharp AT transition exists also for vector spins if the field randomness is isotropic in spin space [102], without a GT precursor [103].…”

Section: Feature Articlementioning

confidence: 99%

A spin glass perspective on ferroic glasses

Sherrington

2014

Physica Status Solidi (b)

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A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities of experimental observations, without considering all possible complexities and alternatives.Comment: Misprint corrected. Now available at http://www.wileyonlinelibrary.com under DOI 10.1002/pssb.20135039

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“…IV we present our analytical work on the mcomponent SK model in the presence of an m-component random field. It has been shown that in the mean-field limit [19] that under the application of a random magnetic field, of variance h 2 r , there is a phase transition line in the h r − T plane, the so-called de Almeida-Thouless (AT) line, across which the critical exponents lie in the Ising AT universality class. Below this line, the ordered phase has full replica symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

Metastable minima of the Heisenberg spin glass in a random magnetic field

2016

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We have studied zero-temperature metastable minima in classical m-vector component spin glasses in the presence of m-component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for m>2. We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the m=2 and m=3 cases in the SK model the final energy reached in the quench is very close to the energy E_{c} at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states ρ(λ) of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual sqrt[λ] form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.

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Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

Cited by 23 publications

References 24 publications

One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses

One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses

A spin glass perspective on ferroic glasses

Metastable minima of the Heisenberg spin glass in a random magnetic field

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