Hyperscaling and the critical exponentv

Abstract

In this paper, we give a detailed discussion of the derivation of the critical exponentv in three dimensions (n=3), starting from the symmetric Landau Hamiltonian. We present a detailed argumentation that explains the nonvalidity of hyperscaling: this follows from a structural aspect of the theory and is not based on the actual numerical values that one obtains. A table with the approximate calculated values of the critical exponents α, ψ,v and η is given forN=0, 1, 2, 3, ∞; hereN is the number of components of the order parameter.