Log-periodic critical amplitudes: a perturbative approach

Abstract

Log-periodic amplitudes appear in the critical behavior of a large class of systems, in particular when a discrete scale invariance is present. Here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial. In this case, the log-periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated.

17 pages, 2 figures

References in corpus (2)

• Heat Kernels and Zeta Functions on Fractals
• Oscillatory critical amplitudes in hierarchical models and the tail of the Harris random variable

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• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• Devil's Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions
• Strong anomalous diffusion of the phase of a chaotic pendulum
• Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model from Renormalization-Group Theory
• Revisiting log-periodic oscillations