Dynamics of rough surfaces generated by two-dimensional lattice spin models

Brito, Alexandre Faissal; Redinz, José Arnaldo; Plascak, J. A.

doi:10.1103/physreve.75.046106

Cited by 16 publications

(10 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a last application, we study the permutation measures and applied to Ising surfaces [40] , [41] . These surfaces are obtained by accumulating the lattice spin values of the Ising model defined by the Hamiltonian.…”

Section: Resultsmentioning

confidence: 99%

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

et al. 2012

View full text Add to dashboard Cite

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable.

show abstract

Section: Resultsmentioning

confidence: 99%

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

et al. 2012

View full text Add to dashboard Cite

show abstract

“…23 Recent works have used the Blume-Capel model to study ferromagnetic thin films using an alternating single-ion anisotropy 24 and the dynamics of rough surfaces. 25 A spatially dependent ⌬ i has been studied in a vector generalization of the Blume-Capel model 26,27 to describe wetting in He 3 -He 4 mixtures. Here ⌬ i takes on separate values in the surface and bulk, and as a consequence the Helium concentration and superfluid order parameter have a nontrivial spatial dependence as one moves away from the boundaries.…”

Section: Model and Calculational Approachmentioning

confidence: 99%

Monte Carlo study of an inhomogeneous Blume-Capel model: A case study of the local density approximation

2008

View full text Add to dashboard Cite

Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns the properties of ultracold optically trapped atoms. Of interest are how the superfluid-insulator transition is modified by the inhomogeneity, and, indeed, the extent to which a sharp transition survives at all. This paper explores a classical analog of these systems, the Blume-Capel model with a spatially varying single-ion anisotropy and/or temperature gradient. We present results both for the nature of the critical properties and for the validity of the "local density approximation" which is often used to model the inhomogeneous case. We compare situations when the underlying uniform transition is first and second orders.

show abstract

“…1. An Ising surface [102,103] is a square lattice in which the height at each lattice site represents the accumulated sum of spin variables of particles in a Monte Carlo simulation [66]. If we assume σ i ∈ {−1, 1} represents the spin variable at site i, we can write the Hamiltonian of this system as…”

Section: Appendix A: Definitions Of Dynamical Systemsmentioning

confidence: 99%

ordpy: A Python package for data analysis with permutation entropy and ordinal network methods

Pessa,

Ribeiro

2021

Preprint

View full text Add to dashboard Cite

Since Bandt and Pompe's seminal work, permutation entropy has been used in several applications and is now an essential tool for time series analysis. Beyond becoming a popular and successful technique, permutation entropy inspired a framework for mapping time series into symbolic sequences that triggered the development of many other tools, including an approach for creating networks from time series known as ordinal networks. Despite the increasing popularity, the computational development of these methods is fragmented, and there were still no efforts focusing on creating a unified software package. Here we present ordpy, a simple and open-source Python module that implements permutation entropy and several of the principal methods related to Bandt and Pompe's framework to analyze time series and two-dimensional data. In particular, ordpy implements permutation entropy, complexity-entropy plane, complexity-entropy curves, missing ordinal patterns, ordinal networks, and missing ordinal transitions for one-dimensional (time series) and two-dimensional (images) data as well as their multiscale generalizations. We review some theoretical aspects of these tools and illustrate the use of ordpy by replicating several literature results.

show abstract

Dynamics of rough surfaces generated by two-dimensional lattice spin models

Cited by 16 publications

References 29 publications

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

Monte Carlo study of an inhomogeneous Blume-Capel model: A case study of the local density approximation

ordpy: A Python package for data analysis with permutation entropy and ordinal network methods

Contact Info

Product

Resources

About