Classical lattice models with single-node interactions on hierarchical lattices: The two-layer Ising model

A.V. Myshlyavtsev, M.D. Myshlyavtseva and S.S. Akimenko

Physica A: Statistical Mechanics and its Applications, 2020, vol. 558, issue C

Abstract: A general approach is proposed for renormalization group transformations at arbitrary hierarchical lattices with two root nodes and the presence of single-node interactions (interactions between layers, magnetic field, chemical potential, etc.). The effectiveness of the proposed approach was shown for the two-layer Ising model in a zero magnetic field on the simplest representative of folded square hierarchical lattices. The phase diagram was investigated and the shift exponent (φ) was calculated at various values of the interaction energy in each layer (J1,J2) and between the layers (J3). The value φ≈ 2.41 was obtained for identical interactions in the layers (J1= J2). In the remaining cases (J1≠J2) the shift exponent turned out to be close to 0.5, which is consistent with the data for the square lattice. The exceptional case is J1 > 0, J2> 0, and J1 ≠J2, where the transition shift exponent in the second layer takes the value 2.57.

Keywords: Two-layer Ising model; Hierarchical lattice; Critical temperature; Shift exponent; Single-node interaction; Renormalization group (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437120304751
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120304751

DOI: 10.1016/j.physa.2020.124919

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().