Numerical study of a short-range<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-spin glass model in three dimensions

Campellone, Matteo; Coluzzi, Barbara; Parisi, Giorgio

doi:10.1103/physrevb.58.12081

Cited by 30 publications

(62 citation statements)

References 30 publications

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“…We have also found this behavior in more general constraint satisfaction problems than K-COL and K-SAT [50]. Relaxation behavior similar to that in our models has also been obtained by Campellone et al for a short-range p-spin glass model [60]. These models should be studied further.…”

Section: Conclusion and Discussionsupporting

confidence: 88%

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 Discussionsupporting

confidence: 88%

Relaxation in graph coloring and satisfiability problems

Svenson

Nordahl

1999

Phys. Rev. E

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“…The position of the maximum of the scaled data yields a value of C ≃ 0.17 and g max ≃ 0.2. This value is universal along the critical line and approximately coincides with the value of the Binder parameter at the tricritical point [8]. Although we expect that the critical line will have some L dependence, very similar results obtained for L = 5 indicate that our estimate of the critical line for L = 6 is a good estimate of the true (infinite volume) line.…”

supporting

confidence: 80%

“…So the presence of a maximum in g(ǫ, T ) already for small sizes is a main feature of this model. For L = 3, 4, 5 finite-size corrections appear to be quite strong (this was already observed in [8] by measuring the P (q)) and the position of the maximum of the Binder parameter as well as its value both shift with L. Nevertheless, the maximum of the Binder parameter for L = 6 superimposes with the maximum for L = 5 and the Binder parameter goes to zero outside from the maximum as L increases. This result indicates the presence of a critical line which separates two paramagnetic phases.…”

mentioning

confidence: 53%

“…Again, this result has been obtained within the mean-field approximation and it is unclear to what extent this result is valid in a finite-dimensional model. Recent numerical simulations on a short-range version of p-spin Ising spin glass [8,9] have shown that the mean-field discontinuous transition becomes continuous in finite dimensions . So the characteristic first-order transition predicted within mean-field theory dramatically changes in finite dimensions.…”

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confidence: 99%

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Complexity and line of critical points in a short-range spin-glass model

Campellone¹,

Ritort

2000

Physica A: Statistical Mechanics and its Applications

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We investigate the critical behavior of a three-dimensional short-range spin glass model in the presence of an external field ǫ conjugated to the Edwards-Anderson order parameter. In the meanfield approximation this model is described by the Adam-Gibbs-DiMarzio approach for the glass transition. By Monte Carlo numerical simulations we find indications for the existence of a line of critical points in the plane (ǫ, T ) which separates two paramagnetic phases and terminates in a critical endpoint. This line of critical points appears due to the large degeneracy of metastable states present in the system (configurational entropy) and is reminiscent of the first-order phase transition present in the mean-field limit. We propose a scenario for the spin-glass transition at ǫ = 0, driven by a spinodal point present above Tc, which induces strong metastability through Griffiths singularities effects and induces the absence of a two-step shape relaxation curve characteristic of glasses.Among all different approaches to understand the glass transition the thermodynamic theory of Adam-Gibbs-Di Marzio (AGM) has deserved a lot of interest during the last decades [1]. The AGM theory predicts the occurrence, at a Kauzmann temperature T K , of a second order phase transition for the metastable undercooled liquid where the configurational entropy (also called complexity) vanishes. The validity of the AGM theory for real glasses has never been demonstrated so the correct description of the glass transition still remains open [2]. An alternative dynamical approach was proposed in the eighties to describe relaxational processes in the undercooled liquid regime, experimentally observed in scattering and dielectric measurements. This received the name of mode-coupling theory (MCT) [3].Quite recently it has been realized that spin glasses are models which account for both the thermodynamic (AGM) and the dynamical (MCT) approaches [4]. Although spin glasses are models with quenched disorder (and structural glasses are not) this is not an essential difference because the existence of a crystal phase in structural glasses has no dramatic effect in the dynamics of the (disordered) metastable undercooled liquid phase. Unfortunately, up to now this connection between spinglasses and glasses remains only at the mean-field level and it is not clear what happens if one considers shortrange interactions. In fact, concepts such as complexity in AGM or the ergodicity parameter in ideal MCT are originally mean-field and it is not clear what is their relevance in short-ranged realistic systems.Recently it has been suggested [6,5] that the effect of the complexity could be observed through numerical simulations in a generic glassy system coupling two replicas by introducing a term in the Hamiltonian of the type −ǫq (ǫ being the conjugate field of the order parameter q which is the overlap between the configurations of the two replicas [7]). Through the study of an exactly solvable spin-glass model it has been shown the existence of a first order tra...

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“…This explains the non-positiveness of the Binder cumulant in Potts glasses and p-spin models. The same being also true for p even when there is time-reversal symmetry 4 .…”

Section: Introductionmentioning

confidence: 58%

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

2001

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The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in 2 which show that two of these parameters, G and Gc, take universal values in the limT →0. In this paper we present a detailed study of parameters measuring OPF for two meanfield models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p=3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for Tc and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at.

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Numerical study of a short-rangep-spin glass model in three dimensions

Cited by 30 publications

References 30 publications

Relaxation in graph coloring and satisfiability problems

Relaxation in graph coloring and satisfiability problems

Complexity and line of critical points in a short-range spin-glass model

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

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