https://doi.org/10.1140/epjp/s13360-024-05190-3
Regular Article
Phase diagrams and thermodynamic study of the mixed spin-1/2 and spin-3 Blume-Capel model: renormalization group theory
1
LS2ME Laboratory, Polydisciplinary Faculty, Sultan Moulay Slimane University, 25000, Khouribga, Morocco
2
LPMC Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, 24000, El Jadida, Morocco
Received:
7
February
2024
Accepted:
16
April
2024
Published online:
6
May
2024
In this work, we study the Blume-Capel model of a mixed spin system (
and 
) 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 
, above which the critical behavior of the system changes; therefore, we can distinguish two possible cases, one when 
and the other when 
. Considering 
and 
, 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 
and 
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.
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