Semi-infinite mixed spin-1/2 and spin-5/2 Blume–Capel model by renormalization group theory and Monte Carlo simulation

Using the renormalization group (RG) theory and Monte Carlo simulation (MCS), the semi-infinite mixed spin-1/2 and spin-5/2 Blume–Capel system has been studied. Depending on the ratios (bulk–surface) R and D, four qualitative types of phase diagrams are determined and classified; each type is characterized by the presence or not of ordinary, extraordinary, surface and special phase transitions. To show the critical behavior of this system at the vicinity of the first-order transitions at low temperature using RG theory, we have plotted the variations of the bulk and surface free energy derivatives. We have also given the associated fixed points and the critical exponents showing the different classes of universality at the surface. In addition, the distribution of the different types of phase diagrams in the (R, D) plane is given exhibiting the existence of a critical value R_C = 0.57 delimiting two types on each side. The MCS method is also employed to validate the results obtained by the RG theory. To confirm the critical behavior of the system near the first-order transitions at low temperature using MCS, we have presented the variations of the bulk and surface magnetizations per site. Finally, this work is completed by discussions and comparisons.