Two-parameter scaling of correlation functions near continuous phase transitions

Abstract

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

References in corpus (13)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• The transition temperature of the dilute interacting Bose gas
• The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Self-energy and critical temperature of weakly interacting bosons
• Crossover critical behavior in the three-dimensional Ising model
• Classical-to-critical crossovers from field theory
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Monte Carlo investigations of phase transitions: status and perspectives

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