Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons

Abstract

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2\pi \rho$. For irrational $\rho$, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.

revised version accepted for publication in Phys. Rev. Lett

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• Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation
• Effect of random antiferromagnetic exchange on the spin waves in a three-dimensional Heisenberg ferromagnet