The spin-2 Blume-Capel model by position space renormalization group

Abstract

Using the renormalization group approximation and specifically the Migdal-Kadanoff technique, we study the spin-2 Blume-Capel model on d-dimensional hypercubic lattice. The phase diagram at the ground state of this model is determined. For T≠0K, we give also the phase diagram in the (temperature, anisotropy) plane, with first and second-order phase transitions and tricritical points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d=2 and d=3. Finally, this work is completed by a discussion and comparison with other approximation.