Critical point phenomena, heat capacities and the renormalization group theory of fluctuations

Abstract

In the normal study of matter, the ordered state is considered first, followed by the addition of minor disorder or fluctuations, for instance, studying crystalline solids with some quasiparticle excitations like phonons and magnons. The discovery of the universality of critical point phenomena seems to provide a chance to study a regime dominated by the fluctuations. The Onsager solution of the two-dimensional Ising model, exhibiting a logarithmic singularity in heat capacity, and the Fairbank-Buckingham-Kellers experiments, showing such a singularity in the heat capacity near the superfluid transition of liquid ⁴He, are landmarks in this topic. The recent renormalization group theory shows a way of studying the patterns among the fluctuations. The dependence of the critical exponents upon spatial and spin dimensionalities, the existence of universal amplitude ratios and the other aspects of critical phenomena are briefly discussed.