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Open AccessFeature PaperArticle

Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice

Department of Theoretical Physics and Astrophysics, Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic
Entropy 2018, 20(2), 91; https://doi.org/10.3390/e20020091
Received: 30 December 2017 / Revised: 26 January 2018 / Accepted: 26 January 2018 / Published: 29 January 2018
(This article belongs to the Special Issue New Trends in Statistical Physics of Complex Systems)
The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S. View Full-Text
Keywords: mixed-spin ising model; triplet interaction; weak-universal critical behaviour mixed-spin ising model; triplet interaction; weak-universal critical behaviour
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MDPI and ACS Style

Strečka, J. Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice. Entropy 2018, 20, 91. https://doi.org/10.3390/e20020091

AMA Style

Strečka J. Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice. Entropy. 2018; 20(2):91. https://doi.org/10.3390/e20020091

Chicago/Turabian Style

Strečka, Jozef. 2018. "Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice" Entropy 20, no. 2: 91. https://doi.org/10.3390/e20020091

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