The two-layer Ising model on a sequence of diamond-like hierarchical lattices

Anisimova, G. D.; Myshlyavtsev, A. V.; Akimenko, S. S.

doi:10.1016/j.physa.2021.126341

Cited by 3 publications

(1 citation statement)

References 52 publications

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“…, By direct calculations we get that tφ (x (1) * ) < 1 and tφ t (x (2) * ) > 1, see figure 4. Hence, x (1) * is stable, whereas x (2) * is unstable. This means that lim…”

Section: D(tq) D(t)d(q)mentioning

confidence: 99%

Phase transitions in the Ising model on a hierarchical random graph based on the triangle

Kotorowicz

Kozitsky

2022

J. Phys. A: Math. Theor.

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Hierarchical graphs were invented to formalize heuristic Migdal-Kadanoff renormalization arguments. In such graphs, certain characteristic patterns (motifs) appear as construction elements. Real-world complex networks may also contain such patterns. S. Itzkovitz and U. Alon in Phys. Rev. E, 2005, 71, selected five most typical motifs, which include the triangle. In Cond. Matt. Phys., 2011, 14, M. Kotorowicz and Yu. Kozitsky introduced and described hierarchical random graphs in which these five motifs appear at each hierarchy level. In the present work, we study the equilibrium states of the Ising spin model living on the graph of this kind based on the triangle. The main result is the description of annealed phase transitions in this model. In particular, we show that -- depending on the parameters -- the model may be in an unordered or ordered states at all temperatures, as well as to have a critical point. The key aspect of our theory is detecting the appearance of an ordered state by the non-ergodicity of a certain nonhomogeneous Markov chain.

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“…, By direct calculations we get that tφ (x (1) * ) < 1 and tφ t (x (2) * ) > 1, see figure 4. Hence, x (1) * is stable, whereas x (2) * is unstable. This means that lim…”

Section: D(tq) D(t)d(q)mentioning

confidence: 99%

Phase transitions in the Ising model on a hierarchical random graph based on the triangle

Kotorowicz

Kozitsky

2022

J. Phys. A: Math. Theor.

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Enumeration Of Subtrees Of Two Families Of Self-Similar Networks Based On Novel Two-Forest Dual Transformations

Sun,

Liu,

Yang

et al. 2023

The Computer Journal

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As a structural topological index, the number of subtrees has great significance for the analysis and design of hybrid locally reliable networks. In this paper, with generating function and introducing a novel two-forest dual transformation technique, we solve the subtree enumerating problems of two representatives of the self-similar networks, such as the hierarchical lattice and $(u,v)$-flower networks. Moreover, by means of the circle weight transfer technique, two linear time algorithms of computing the subtree generation functions of these two families of networks are also proposed. The subtree density of two special cases for these self-similar networks is briefly discussed as an application.

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Tensor networks for hierarchical lattices

Akimenko,

Myshlyavtsev

2024

EPL

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In this paper, we propose an approach to obtain numerically exact solutions for hierarchical lattices by representing them as a tensor network. The visual representation of these networks greatly simplifies the computational algorithm. Furthermore, we introduce a method for incorporating single-node interactions, enabling us to disregard the inhomogeneity of the hierarchical lattice nodes and simulate the behavior on a regular lattice instead. This methodology allows for qualitative studies of the phase space of desired lattice models with single-node interactions, which holds relevance for adsorption systems. The efficiency of the approach is demonstrated using the Ising model and the binary gas adsorption model as examples.

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The two-layer Ising model on a sequence of diamond-like hierarchical lattices

Cited by 3 publications

References 52 publications

Phase transitions in the Ising model on a hierarchical random graph based on the triangle

Phase transitions in the Ising model on a hierarchical random graph based on the triangle

Enumeration Of Subtrees Of Two Families Of Self-Similar Networks Based On Novel Two-Forest Dual Transformations

Tensor networks for hierarchical lattices

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