Microscopic realizations of the trap model

Junier, Ivan; Kurchan, Jorge

doi:10.1088/0305-4470/37/13/003

Cited by 16 publications

(36 citation statements)

References 27 publications

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“…Out-of-equilibrium FDR for K ≪ N Let us consider now the intermediate dynamics 1 ≪ K ≪ N . In the case T > T g /2, one recovers when K/N → 0 the same behavior as for K = 1 [21], namely a linear FDR with a slope equal to 1/T , where T is the heat bath temperature. Thus there is no violation of fluctuation-dissipation theorem, as seen on Fig.…”

Section: Fluctuation-dissipation Relationssupporting

confidence: 52%

“…The glass transition in the present model resembles the standard REM transition, the only difference being that the former is first order whereas the latter is second order [12,21]. In particular, an important property shared by both models is that for low energy states, magnetization and energy become decorrelated.…”

Section: Optimization and Spin Modelmentioning

confidence: 60%

“…The first result is that some particular dynamical rules lead to the behaviors found in both usual trap models: the case K = 1 yields the activated trap model proposed by Bouchaud (BTM), whereas the model with K = N can be mapped onto the entropic version studied by Barrat and Mézard (BMM). The former case has already been studied in [21], but was recalled here for the sake of completeness.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we consider the study of a system defined by such an Hamiltonian. In this system, energies E < k ln N (where k is some positive constant) are independent random variables [21,22] that are distributed according to (assuming N ≫ 1):…”

Section: Optimization and Spin Modelmentioning

confidence: 99%

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Dynamic phase diagram of the number partitioning problem

Junier

Bertin

2004

Phys. Rev. E

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We study the dynamic phase diagram of a spin model associated with the Number Partitioning Problem, as a function of temperature and of the fraction K/N of spins allowed to flip simultaneously. The case K = 1 reproduces the activated behavior of Bouchaud's trap model, whereas the opposite limit K = N can be mapped onto the entropic trap model proposed by Barrat and Mézard. In the intermediate case 1 ≪ K ≪ N , the dynamics corresponds to a modified version of the Barrat and Mézard model, which includes a slow (rather than instantaneous) decorrelation at each step. A transition from an activated regime to an entropic one is observed at temperature Tg/2 in agreement with recent work on this model. Ergodicity breaking occurs for T < Tg/2 in the thermodynamic limit, if K/N → 0. In this temperature range, the model exhibits a non trivial fluctuation-dissipation relation leading for K ≪ N to a single effective temperature equal to Tg/2. These results give new insights on the relevance and limitations of the picture proposed by simple trap models.

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Section: Fluctuation-dissipation Relationssupporting

confidence: 52%

Section: Optimization and Spin Modelmentioning

confidence: 60%

Section: Discussionmentioning

confidence: 99%

Section: Optimization and Spin Modelmentioning

confidence: 99%

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Dynamic phase diagram of the number partitioning problem

Junier

Bertin

2004

Phys. Rev. E

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“…(2), were first studied in the context of magnetic hysteresis [13,14]. The phase transitions that get induced by the driving fields in these models were recently investigated too [15].…”

Section: Inducing New Fixed Pointsmentioning

confidence: 99%

Phase transitions in periodically driven macroscopic systems

Dutta

2004

Phys. Rev. E

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We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of certain other equilibrium systems. We then illustrate with a few examples how the conventional knowledge of the equilibrium systems can be made use in choosing the driving fields to engineer new phases and to induce new phase transitions.

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Poisson convergence in the restricted k‐partitioning problem

Bovier¹,

Kurkova²

2006

Random Struct Algorithms

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ABSTRACT:The randomized k-number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k-partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k > 2 in the restricted problem and show that the vector of differences between the k sums converges to a k − 1-dimensional Poisson point process.

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Microscopic realizations of the trap model

Cited by 16 publications

References 27 publications

Dynamic phase diagram of the number partitioning problem

Dynamic phase diagram of the number partitioning problem

Phase transitions in periodically driven macroscopic systems

Poisson convergence in the restricted k‐partitioning problem

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