Glassy behaviour and semi-local invariance in Ising model with four-spin interaction

Lipowski, Adam

doi:10.1088/0305-4470/30/21/012

Cited by 59 publications

(130 citation statements)

References 16 publications

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“…At T g the autocorrelation time is expected to diverge because of the onset of the slow dynamics which turns the stretched exponential behaviour into a power law (with a small exponent) or a logarithm. Although that result is in good agreement with previous simulations [9], [11] the method relying on the stretched exponential fit may prove to be too risky for an exact prediction of T g due to ambiguities in the fitting process and perhaps is not trustable to that accuracy. As an alternative and a cross check, for two different temperature values, namely T = 1.720 and T = 1.695 we show the behaviour of the C spin for two very different values of the waiting time, t w = 300, 2000.…”

Section: Introductionsupporting

confidence: 87%

“…It is well known that this model exhibits a first order phase transition at T c = 1.95 along with a dynamical transition at T g ∼ 1.7, which is the temperature where the glassy behaviour shows up [9], [10], [11]. Even though our main interest is the study of the glassy characteristics by looking at the relaxation as well as the autocorrelation of the order parameters (to be defined below) in the glassy phase, the region T g < T < T c is interesting as well.…”

Section: Introductionmentioning

confidence: 99%

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Slow dynamics in the three-dimensional gonihedric model

et al. 2002

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We study dynamical aspects of three-dimensional gonihedric spins by using Monte-Carlo methods. The interest of this family of models (parametrized by one self-avoidance parameter κ) lies in their capability to show remarkably slow dynamics and seemingly glassy behaviour below a certain temperature T g without the need of introducing disorder of any kind. We consider first a hamiltonian that takes into account only a four-spin term (κ = 0), where a first order phase transition is well established. By studying the relaxation properties at low temperatures we confirm that the model exhibits two distinct regimes. For T g < T < T c , with long lived metastability and a supercooled phase, the approach to equilibrium is well described by a stretched exponential. For T < T g the dynamics appears to be logarithmic. We provide an accurate determination of T g . We also determine the evolution of particularly long lived configurations. Next, we consider the case κ = 1, where the plaquette term is absent and the gonihedric action consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbour interactions. This model exhibits a second order phase transition. The consideration of the relaxation time for configurations in the cold phase reveals the presence of slow dynamics and glassy behaviour for any T < T c . Type II aging features are exhibited by this model.

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Section: Introductionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Slow dynamics in the three-dimensional gonihedric model

et al. 2002

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“…3b). Similar trapping of the system in a metastable state was observed in the three-dimensional plaquette model [11]. Energetic barriers separating metastable states from one another and from the ground states are high: for p = 3, m = 1 the distribution of hyperedges obeys the power scaling law For p = 3, m = 2 the models with random and ferromagnetic initial conditions behave in a qualitatively similar way.…”

Section: Modelsupporting

confidence: 61%

Monte Carlo Studies of the p-Spin Models οn Scale-Free Hypernetworks

Krawiecki

2013

Acta Phys. Pol. A

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Results of Monte Carlo simulations of p-spin models on scale-free hypernetworks are presented. The hypernetworks are obtained using the preferential attachment algorithm, the spins are located in the nodes and the hyperedges connecting p nodes correspond to non-zero ferromagnetic interactions involving p spins. Such models show high degeneracy of the ground state: apart from the ferromagnetic state, depending on the parameters of the preferential attachment algorithm leading to dierent topologies of the obtained hypernetworks, there are several or even innitely many disordered (glassy) states with the same energy. For various network topologies quantities such as the specic heat or magnetic susceptibility show maxima as functions of the temperature, which suggests the occurrence of the glassy or ferromagnetic phase transition. The models under study may serve as a starting point for modelling various forms of cooperation in social and economic sciences involving many-body rather than two-body interactions.

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“…In general, outside the field of disordered systems Ising models with multispin interactions have been less explored [6,7], both because such interactions are less common in real materials and also because in many cases such models display first-order transitions. These might be regarded as a priori less promising subjects for numerical investigation, although the general scaling theory for first-order transitions, initiated in [8][9][10] and developed further in [11][12][13][14][15] and [16][17][18][19], is now generally well-understood.…”

Section: Introductionmentioning

confidence: 99%

“…In the isotropic case we would expect m x abs = m y abs = m z abs and similarly for the squared quantities. Lipowski had previously suggested [6] using an order parameter akin to m sq in equation (31).…”

mentioning

confidence: 99%

Plaquette Ising models, degeneracy and scaling

Johnston¹,

Mueller

Janke

2017

Eur. Phys. J. Spec. Top.

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Abstract. We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour ∝ 1/L 3 to 1/L 2 . The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.

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Glassy behaviour and semi-local invariance in Ising model with four-spin interaction

Cited by 59 publications

References 16 publications

Slow dynamics in the three-dimensional gonihedric model

Slow dynamics in the three-dimensional gonihedric model

Monte Carlo Studies of the p-Spin Models οn Scale-Free Hypernetworks

Plaquette Ising models, degeneracy and scaling

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