Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions

Shore, Joel D.; Holzer, Mark; Sethna, James P.

doi:10.1103/physrevb.46.11376

Cited by 106 publications

(154 citation statements)

References 61 publications

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“…The free energy barriers in these problems have a less pronounced energy dependence than in other models. One can compare them to systems where logarithmic relaxation has been found for T = 0 and T = 0 MC simulations, such as in [55], where a tiling model containing no randomness at all was studied. The main difference between these systems and ours seems to be that they have local interactions and frustration, whereas we have infinite-range interactions and frustration.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Relaxation in graph coloring and satisfiability problems

Svenson

Nordahl

1999

Phys. Rev. E

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Using T = 0 Monte Carlo simulation, we study the relaxation of graph coloring (K-COL) and satisfiability (K-SAT), two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied. A change from exponentially fast to power law relaxation, and a transition to freezing behavior are found. These changes take place for smaller values of the parameter than the solvability transition. Results for the coloring problem for colorable and clustered graphs and for the fraction of persistent spins for satisfiability are also presented.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Relaxation in graph coloring and satisfiability problems

Svenson

Nordahl

1999

Phys. Rev. E

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“…Related aspects of slow evolution in three dimensions were discussed for the homogeneous kinetic Ising ferromagnet [28] and for a kinetic Ising system with competing ferromagnetic and antiferromagnetic interactions [29]. Figure 9 shows simulation data for the first-passage time from the fully-deflated to the fully-inflated state in two and three dimensions.…”

Section: A Relaxation Of Blinker Configurationsmentioning

confidence: 99%

Zero-temperature relaxation of three-dimensional Ising ferromagnets

2011

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We investigate the properties of the Ising-Glauber model on a periodic cubic lattice of linear dimension L after a quench to zero temperature. The resulting evolution is extremely slow, with long periods of wandering on constant energy plateaux, punctuated by occasional energy-decreasing spin-flip events. The characteristic time scale τ for this relaxation grows exponentially with the system size; we provide a heuristic and numerical evidence that τ ∼ exp(L 2 ). For all but the smallest-size systems, the long-time state is almost never static. Instead the system contains a small number of "blinker" spins that continue to flip forever with no energy cost. Thus the system wanders ad infinitum on a connected set of equal-energy blinker states. These states are composed of two topologically complex interwoven domains of opposite phases. The average genus gL of the domains scales as L γ , with γ ≈ 1.7; thus domains typically have many holes, leading to a "plumber's nightmare" geometry.

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“…It is thus an explicit realization of the constrained dynamics scenario of Palmer et al [14]. Other non-disordered short-range spin systems displaying glassy features are three-dimensional Ising models with competing nearest and next-nearest neighbour interactions [23], or with ferromagnetic four-spin plaquette interactions [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Glassiness and constrained dynamics of a short-range nondisordered spin model

2000

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We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual description in terms of free defects subject to dynamical constraints, and is an explicit realization of the "hierarchically constrained dynamics" scenario for glassy systems. We give a number of exact results for the statics of the model, and study in detail the dynamical behaviour of one-time and two-time quantities. We also consider the role played by the configurational entropy, which can be computed exactly, in the relation between fluctuations and response.

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Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions

Cited by 106 publications

References 61 publications

Relaxation in graph coloring and satisfiability problems

Relaxation in graph coloring and satisfiability problems

Zero-temperature relaxation of three-dimensional Ising ferromagnets

Glassiness and constrained dynamics of a short-range nondisordered spin model

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