On the Yang–Lee edge singularity for Ising model on nonhomogeneous structures

Knežević, Milan; Joksimović, J.; Knežević, Dragica

doi:10.1016/j.physa.2005.11.008

Cited by 4 publications

(7 citation statements)

References 19 publications

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“…As we have shown in this paper, such fluctuations of the local coordination number exert the most direct influence on the nature of the critical singularities in the statistics of lattice animals also. A similar situation arises in the case of the Yang-Lee edge singularity of the ferromagnetic Ising model on a class of non-homogeneous structures [15]. It would be interesting to find some further models of statistical mechanics in which the local lattice inhomogeneities affect their critical behavior so strongly.…”

Section: Discussionmentioning

confidence: 64%

Lattice animals on a class of hierarchical graphs

2007

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We study the statistics of lattice animals on a class of hierarchical graphs whose members can be labeled by a set of integers , g≥1. We have shown that the animal critical behavior crucially depends on the minimal value of these parameters. For we find the usual power-law behavior, while for the associated generating function displays an essential singularity ∼exp[c(tc−t)−ψ], where c is a constant and the exponent ψ is related to the leading correction term in the asymptotic behavior of the number of animal configurations having N bonds, , ω = ψ/(ψ+1). We express the entropic exponent ω and the animal size exponent in terms of pertinent graph parameters.

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Section: Discussionmentioning

confidence: 64%

Lattice animals on a class of hierarchical graphs

2007

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“…The effect of inhomogeneity on the critical behaviour of magnetic systems has been considered in various contexts (e.g. disorder, coupling randomness, quasiperiodic structures); in particular, discrete-spin models defined on fractal topologies possess critical properties significantly different and richer than those found for translationally invariant systems [1,2,3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Metric characterization of cluster dynamics on the Sierpinski gasket

Agliari¹,

Casartelli²,

Vivo³

2010

J. Stat. Mech.

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We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpsinski Gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projection of evolving configurations into an appropriate partition space, where an information-based metrics (Rohlin distance) can be naturally defined and worked out in order to detect the changing and the stable components of clusters. The analysis highlights the existence of different temperature regimes according to the size and the rate of change of clusters. Such regimes are, in turn, related to the correlation length and the emerging "critical" fluctuations, in agreement with previous thermodynamic analysis, hence providing a non-trivial geometric description of the peculiar critical-like behavior exhibited by the system. Moreover, at high temperatures, we highlight the existence of different time scales controlling the evolution towards chaos.

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“…The original YL circle theorem [1,2] is independent of the topological structure of the underlying lattice and should also apply to appropriate models of certain nonhomogeneous or even disordered systems (diluted ferromagnets, for example). In order to understand better certain aspects of their critical behavior, several studies of the density of zeros of the ferromagnetic Ising model on a variety of deterministic fractals have been performed so far [13][14][15][16]. It has been shown that in this case the density of zeros exhibits a scaling form near the edge, which is more complicated than a pure power law.…”

Section: Introductionmentioning

confidence: 99%

“…This seemed rather surprising, due to the fact that these two models do not belong to the same class of universality in the case of homogenous spaces, and those fractals that have a uniform coordination number (3-simplex or usual 2d Sierpinski gasket, for example). Recently [16], we have shown that the two models exhibit the same critical behavior in the case of two 'quasi-linear' [17] self-similar lattices with loops on all spatial scales. This made us believe that it might have not been a pure coincidence, motivating us to explore the YL edge singularity for the Ising model on fractal lattices having better connectivity than those studied previously.…”

Section: Introductionmentioning

confidence: 99%

“…This puzzle is quite similar to the one already encountered in our earlier studies of the YL edge problem for the ferromagnetic Ising model on 'quasi-linear' fractals. As detailed in [15,16], the basic step in a search for the asymptotic form of relevant variables near the edge was the observation that there exists an invariant manifold, all points of which are attracted by a pertinent fixed point. The situation is analogous for recursion relations (1).…”

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confidence: 99%

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The Yang–Lee edge singularity for the Ising model on two Sierpinski fractal lattices

Knežević

2010

J. Phys. A: Math. Theor.

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We study the distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on two Sierpiski-type lattices. We have shown that relevant correlation length displays a logarithmic divergence near the edge, ξ YL ∼ | ln(δh)| where is a constant and δh distance from the edge, in the case of a modified Sierpinski gasket with a nonuniform coordination number. It is demonstrated that this critical behavior can be related to the critical behavior of a simple zero-field Gaussian model of the same structure. We have shown that there is no such connection between these two models on a second lattice that has a uniform coordination number. These findings suggest that fluctuations of the lattice coordination number of a nonhomogeneous selfsimilar structure exert the crucial influence on the critical behavior of both models.

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On the Yang–Lee edge singularity for Ising model on nonhomogeneous structures

Cited by 4 publications

References 19 publications

Lattice animals on a class of hierarchical graphs

Lattice animals on a class of hierarchical graphs

Metric characterization of cluster dynamics on the Sierpinski gasket

The Yang–Lee edge singularity for the Ising model on two Sierpinski fractal lattices

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