Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena

Abstract

Concepts of skeleton order parameters and their conjugate symmetry breaking skeleton fields are introduced in order to describe the phase transition of the relevant system. It is shown that the skeletonization of Hamiltonians is very useful in understanding the essence of phase transitions. Singularities of skeleton susceptibilities are studied in general. There are given some examples in spin systems. Fluctuating mean-field approximations are introduced to study phase transitions qualitatively, namely to find more accurate values of critical points even in frustrated spin systems. This idea gives the basis of the coherent anomaly method (CAM). This new method is explained briefly to obtain non-classical critical exponents in cluster mean-field approximations on the basis of the concept of coherent anomalies.