Semi-infinite Ising model by the Renormalization Group

The renormalization method gives us the opportunity to understand the existence of the scale laws. In addition thanks to the hypotheses of homogeneities which are verified by this renormalization transformation. We establish relationships between critical exponents and consequently describe the state of the system at the critical point. Also we can see that despite having approximations the renormalization group transformations lead directly to critical exponent values close to the exact values. More recently calculations using very sophisticated mathematical techniques have enabled this method to obtain precise quantitative predictions of the critical exponents which are in agreement with the experimental values. Besides understanding this method opens the way for researchers to study the magnetic properties of different structures and lead to predict new materials and nanomaterials by the density functional theory (DFT) or by the Monte Carlo simulation method (MCS).