Ising ferromagnet on a fractal family: Thermodynamical functions and scaling laws

Redinz, José Arnaldo; Magalhaes, A C N de

doi:10.1103/physrevb.51.2930

Cited by 10 publications

(10 citation statements)

References 17 publications

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“…Somewhat larger deviations above 0.036 are provided by the fits within L ≥ 64, shown in Fig. 5, at approximately estimated values β c = 0.2216546234(99) and β c = 0.221654615 (13) of the critical coupling.…”

Section: Tests Of the Rg Exponentsmentioning

confidence: 80%

“…The dashed line shows the fit with only the leading correction term (the term with coefficient a 1 ) to β c − β c included, whereas the solid line -the fit with both correction terms. These fits give β c = 0.2216546234(99) and β c = 0.221654615 (13), respectively. The χ 2 /d.o.f.…”

Section: Estimation Of the Critical Couplingmentioning

confidence: 95%

“…Today, we see a growing interest in the application of MC-based non-perturbative approaches and the development of powerful MC simulation tools for 3D systems [11,12]. The exact non-perturbative RG equations are known for various models on fractal lattices (see, e.g., [13] and references therein). Moreover, a rigorous RG analysis has been made in four dimensions (see, e.g., [14]).…”

Section: Introductionmentioning

confidence: 99%

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Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

2022

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Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry are considered. Starting with Goldstone mode singularities in the XY and O(4) models, we briefly review various theoretical concepts, as well as state-of-the-art Monte Carlo simulation results. They support recent results of the GFD (grouping of Feynman diagrams) theory, stating that these singularities are described by certain nontrivial exponents, which differ from those predicted earlier by perturbative treatments. Furthermore, we present the recent Monte Carlo simulation results of the three-dimensional Ising model for lattices with linear sizes up to L = 1536, which are very large as compared to L ≤ 128 usually used in the finite-size scaling analysis. These results are obtained, using a parallel OpenMP implementation of the Wolff single-cluster algorithm. The finite-size scaling analysis of the critical exponent η, assuming the usually accepted correction-to-scaling exponent ω ≈ 0.8, shows that η is likely to be somewhat larger than the value 0.0335 ± 0.0025 of the perturbative renormalization group (RG) theory. Moreover, we have found that the actual data can be well described by different critical exponents: η = ω =1/8 and ν = 2/3, found within the GFD theory.

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Section: Tests Of the Rg Exponentsmentioning

confidence: 80%

Section: Estimation Of the Critical Couplingmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

2022

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“…In this case no appropriate family of lattices could be found, providing the critical exponents as (almost) continuous functions of d in agreement with such an analytic continuation. A family of fractal lattices, which allows to treat d as a continuous parameter in exact recurrence relations, has been considered in [15]. However, these lattices are not quite appropriate to mimic an analytic continuation from d-dimensional hypercubes.…”

Section: Problem Of An Analytic Continuation Of the Critical Exponentsmentioning

confidence: 99%

SURFACE TENSION AND INTERFACIAL FLUCTUATIONS IN d-DIMENSIONAL ISING MODEL

Kaupužs

2005

Int. J. Mod. Phys. C

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The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d − 1)dimensional interface splits in disconnected pieces. Some phenomenological arguments are proposed to describe such interfaces. They show that the character of the interfacial fluctuations at d < 2 is not the same as provided by a formal analytic continuation from d-dimensional hypercubes with d ≥ 2. It, probably, is true also for the related critical exponents.

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“…Two main formulations of the non-perturbative RG [the Wilson approach (also called Wilson-Polchinski) and the "effective average action" approach] are discussed in resent publications [15][16][17][18]. The exact non-perturbative RG equations are known for various models on fractal lattices (see, for example, [19] and references therein). Moreover, a rigorous RG analysis has been made in four dimensions [20].…”

Section: Introductionmentioning

confidence: 99%

Order parameter of a three-dimensional Ising-like system in the simplest and higher non-Gaussian approximations

Pylyuk¹

2013

Condens. Matter Phys.

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The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order parameter (the average spin moment) of a three-dimensional uniaxial magnet are obtained in approximations of quartic and sextic non-Gaussian fluctuation distributions (the ρ 4 and ρ 6 models, respectively), taking into account confluent corrections. Some distinctive features appearing in the process of calculating the order parameter on the basis of two successive non-Gaussian approximations are indicated. The dependence of the average spin moment of an Ising-like system on the temperature and microscopic parameters is studied.

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Ising ferromagnet on a fractal family: Thermodynamical functions and scaling laws

Cited by 10 publications

References 17 publications

Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches

SURFACE TENSION AND INTERFACIAL FLUCTUATIONS IN d-DIMENSIONAL ISING MODEL

Order parameter of a three-dimensional Ising-like system in the simplest and higher non-Gaussian approximations

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