The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system

Akın, Hasan

doi:10.1016/j.chaos.2022.113086

Cited by 12 publications

(11 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This query prompts an exploration into the regions lying outside the depicted surface (see [6] for details). Investigating whether a phase transition manifests in these uncharted territories involves delving into the behavior of the model under different combinations of J and T. It calls for an examination of the system's response to varying conditions beyond the scope of the illustrated surface.…”

Section: 1 H H H H H H Hmentioning

confidence: 99%

“…In recent times, significant progress has been made in exploring mixed-spin Ising models on the CT, demonstrating the occurrence of phase transition phenomena [24,25]. Yet, an unresolved question remains regarding whether this model exhibits a phase transition in the mixed-spin state.…”

Section: 1 H H H H H H Hmentioning

confidence: 99%

“…In this section, we will use the second approach (the recurrence relation [4]) to analyze the properties of GMs for the model. Computing the partition function is usually a difficult computational task since it requires evaluating the sum on the right side, which might require counting items with complex combinatorial properties [5,6]. We shall calculate it by using a tree-graph that branches out from any given site as an approximation of the lattice.…”

Section: The Limiting Gibbs Measures Associated With 1d Potts-sos Modelmentioning

confidence: 99%

“…In [6], the authors have successfully addressed and resolved the phase transition problem for the q-state Potts model on a Cayley tree (CT) of any order. Their work involves the comprehensive computation of critical surfaces, which serve as indicators for the occurrence of phase transitions in the model.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

Akın

2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this investigation, we consider the one-dimensional (1D) mixed-type Potts-SOS model, where the spin is within the range of $\{-1, 0, 1\}$. We elaborate thermodynamic characteristics of 1D Potts-SOS model through the application of three distinct analytical approaches. We provide a brief overview of all translation-invariant splitting Gibbs measures (TISGMs) applicable to this model. For the model with a boundary field condition, we provide a comprehensive analysis of the uniqueness and non-uniqueness properties of the subset of fully homogeneous splitting Gibbs masures (SGMs). Our demonstration reveals that the model under consideration does not exhibit a phase transition phenomenon. We are also curious in the stability study of the suggested fixed points associated with the Gibbs measures. We show that the magnetization decreases to zero. By means of the transfer matrix method, we compute the free energy, entropy and internal energy of the model.

show abstract

Section: 1 H H H H H H Hmentioning

confidence: 99%

Section: 1 H H H H H H Hmentioning

confidence: 99%

Section: The Limiting Gibbs Measures Associated With 1d Potts-sos Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

Akın

2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In Ref. [17], by means of the KCC we studied (2,1/2)-MSIM on CT of second-order and showed numerically that the model displays chaotic behavior in several regimes.…”

Section: Introductionmentioning

confidence: 99%

The Extremality of Disordered Phases for the Mixed Spin-(1,1/2) Ising Model on Cayley Tree of Arbitrary Order

Akın

Mukhamedov

2023

Preprint

View full text Add to dashboard Cite

The aim of this paper is to continue the investigation into the set of translation-invariant splitting Gibbs measures (TISGMs) for Ising model having the mixed spin (1,1/2) (shortly, (1,1/2)-MSIM) on a Cayley tree of arbitrary order. In our previous work [Akın and Mukhamedov, J. Stat. Mech. (2022) 053204], we provided a thorough explanation of the TISGMs, and studied the extremality of disordered phases using a Markov chain with a tree index on a semi-finite Cayley tree with order two. In this paper, we construct the TISGMs and tree-indexed Markov chains associated with to the model. Considering a tree-indexed Markov chain on a Cayley tree of any order, we clarify the extremality of the related disordered phases. By using the Kesten-Stigum condition (KSC), we investigate non-extremality of the disordered phases by means of the eigenvalues of the stochastic matrix associated with (1,1/2)-MSIM on a CT of order k≥2.

show abstract

Towards Enhanced Energy Aware Resource Optimization for Edge Devices Through Multi-cluster Communication Systems

Li,

Ma,

Zhang

et al. 2024

J Grid Computing

View full text Add to dashboard Cite

The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system

Cited by 12 publications

References 31 publications

The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

The Extremality of Disordered Phases for the Mixed Spin-(1,1/2) Ising Model on Cayley Tree of Arbitrary Order

Towards Enhanced Energy Aware Resource Optimization for Edge Devices Through Multi-cluster Communication Systems

Contact Info

Product

Resources

About