Fractals at T=Tc due to instanton-like configurations

Abstract

We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point ($T=T_c$) we show that instanton-like configurations, corresponding to the minima of the effective action functional, build up clusters with fractal geometry characterizing locally the critical fluctuations. The connection between the corresponding (local) fractal dimension and the critical exponents is derived. Possible extension of the local geometry of the system to a global picture is also discussed.

To appear in Physical Review Letters

Cited by in corpus (16)

• Critical Opalescence in Baryonic QCD Matter
• Pion production from a critical QCD phase
• The Fractal Geometry of Critical Systems
• Fractality in momentum space: a signal of criticality in nuclear collisions
• Unorthodox properties of critical clusters
• Generalized Statistical Mechanics at the Onset of Chaos
• Critical fluctuations, intermittent dynamics and Tsallis statistics
• Evolution of Critical Correlations at the QCD Phase Transition
• Evolutionary intermittency and the QCD critical point
• Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation
• Intermittency at critical transitions and aging dynamics at edge of chaos
• Spontaneous Symmetry Breaking in the Phase Space
• An efficient algorithm simulating a macroscopic system at the critical point
• Manifestations of the onset of chaos in condensed matter and complex systems
• Classical evolution of fractal measures generated by a scalar field on the lattice
• Two Dimensional Poincare Maps constructed through Ginzburg-Landau Theory of critical phenomena in Physics