Two-parameter scaling of correlation functions near continuous phase transitions

Hasselmann, Nils; Sinner, Andreas; Kopietz, Peter

Two-parameter scaling of correlation functions near continuous phase transitions

Authors

Hasselmann, Nils

Sinner, Andreas

Kopietz, Peter

Description

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k) = k_c^{-2} g(kξ,k/k_c), where k is the wave-vector, ξis the correlation length, and the interaction-dependent non-universal momentum scale k_c remains finite at the critical fixed point. The correlation function describes the entire critical regime and captures the classical to critical crossover. One-parameter scaling is recovered only in the limit k/k_c->0. We present an approximate calculation of g(x,y) for the Ising universality class using the functional renormalization group.
4 pages, 5 figures, revised version, to appear as Rapid Communication in Phys.Rev.E