Phase diagrams and thermodynamic study of the mixed spin-1/2 and spin-3 Blume-Capel model: renormalization group theory

• Published in: European physical journal plus 2024-05, Vol.139 (5), p.388, Article 388
• Main Authors: Mouhrach, T., Zahir, H., Fathi, A., Sbiaai, K., Bouziani, M. El
• Format: Article
• Language: English
• Subjects: Anisotropy; Applied and Technical Physics; Approximation; Atomic; Complex Systems; Condensed Matter Physics; Critical phenomena; Free energy; Group theory; Information storage; Low temperature; Mathematical and Computational Physics; Molecular; Monte Carlo simulation; Optical and Plasma Physics; Phase diagrams; Phase transitions; Physics; Physics and Astronomy; Regular Article; Statistical physics; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-024-05190-3

In this work, we study the Blume-Capel model of a mixed spin system ( σ = 1 / 2 and S = 3 ) in a hypercubic lattice of dimension d . For this purpose, we choose to work with the renormalization group method, namely the Migdal-Kadanoff technique. The results show that there is a critical dimension d c ≈ 2.14 , above which the critical behavior of the system changes; therefore, we can distinguish two possible cases, one when d < d c and the other when d ≥ d c . Considering d = 2 d < d c and d = 3 d ≥ d c , we identify the stable and unstable fixed points where there is no tricritical point, determine the critical exponents and verify their universal behavior. For the same dimensions, we plot the phase diagrams in the Δ 2 / J , 1 / J and Δ 2 , J planes with a second order transition. Furthermore, we show that at very low temperatures, and by using free energy derivation, three first-order phase transitions can take place.