Critical Phenomena: An Introduction from a Modern Perspective
Power laws are distinctive features of critical phenomena and can be ascribed to diverging length-scales. One of the most important contributions of the studies of critical phenomena is the shift in point of view to a length-scale based analysis and classifying terms of a Hamiltonian as relevant or irrelevant rather than classifying them as numerically weak or strong. The idea of universality transcends the domain of critical phenomena. Critical points are classified by the number of relevant variables required to describe them. A universality class would be described by the exponents and also the amplitude ratios of the various singulax quantities on both sides of the critical point. In a correlation based approach, we need to compute the critical correlations of all possible combinations of the degrees of freedom. Scaling is the rule for criticality, originating from a diverging length scale, while anomalous dimension is seen for fluctuation dominated cases.