Cluster dynamics for randomly frustrated systems with finite connectivity

Persky, N.; Kanter, Ido; Solomon, Sorin

doi:10.1103/physreve.53.1212

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…On φ z graphs we replace 2 → z − 1, which is still in accordance with equs. (3,4). As all even bifurcation points are independent of p, we predict the p independence of the spin glass transition point, as in the more standard approaches.…”

Section: The Saddle Point Equations For Spin Glassessupporting

confidence: 55%

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Spin glasses on thin graphs

et al. 1995

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In a recent paper [1] we found strong evidence from simulations that the Ising antiferromagnet on "thin" random graphs -Feynman diagrams -displayed a mean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field theory results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.We then investigate numerically spin glasses with a ±J bond distribution for the Ising and Q = 3, 4, 10, 50 state Potts models, paying particular attention to the independence of the spin glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution P (q) for all of the models. The parallels with infinite range spin glass models in both the analytical calculations and simulations are pointed out. Submitted to Nucl. Phys. B. [FS]

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Section: The Saddle Point Equations For Spin Glassessupporting

confidence: 55%

“…We thus reproduce the values of β M and β SG calculated from equs. (3,4) for general p as the first two bifurcation points. On φ z graphs we replace 2 → z − 1, which is still in accordance with equs.…”

Section: The Saddle Point Equations For Spin Glassesmentioning

confidence: 99%

Spin glasses on thin graphs

et al. 1995

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“…[21] in alternation with standard Swendsen-Wang [22] cluster updates on each of the replicas. The additional Swendsen-Wang updates are very efficient close to percolation and speed up the simulation considerably [23]. This is an important issue because close to percolation we encounter noticeable finite-size effects, and therefore relatively large lattices have to be simulated to see a good signal for a SG transition below p * .…”

Section: Figmentioning

confidence: 99%

Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings

Jörg

Ricci-Tersenghi

2008

Phys. Rev. Lett.

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We study link-diluted +/-J Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.

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“…In the context of manipulating creative concepts, this translates in very long times for producing really innovative and successful ideas. The usual solution in the context of statistical mechanics is the identication of eective collective degrees of freedom and devising algorithms which act directly in terms of these macroscopic degrees of freedom (macros 4 ). Such procedures replace the slow dynamics based on random walk by a dynamics relying on macroscopic steps.…”

Section: Introductionmentioning

confidence: 99%

“…T h us we w ould reproduce in the NPD context the capability of the cluster-multiscale algorithms to transcend critical slowing down. 4 In order to apply such techniques, one has to ascertain that the system is to a good approximation isolated from external changes and that its global dynamics can be expressed in terms of discrete degrees of freedom. These requirements might seem problematic in the context of marketable products:…”

Section: Introductionmentioning

confidence: 99%

Algorithms for New Product Development: An Exercise in Thought Dynamics

Goldenberg

Horowitz

Mazursky

et al. 1997

Int. J. Mod. Phys. C

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We generate new product ideas using algorithms which manipulate formally conceptual structures. These structures are abstract closed congurations composed of discrete elements which represent parts or properties of the products and of their immediate environment. The algorithms are assembled of a very limited number of fundamental operations acting on the elements. We present some successful eld applications of the method carried out in leading international companies as well as an experiment providing quantitative proof of its superiority o v er usual ideas search.

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Cluster dynamics for randomly frustrated systems with finite connectivity

Cited by 7 publications

References 13 publications

Spin glasses on thin graphs

Spin glasses on thin graphs

Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings

Algorithms for New Product Development: An Exercise in Thought Dynamics

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