Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons
Rafael M. Fernandes, Jörg Schmalian
DOI 10.1103/PhysRevLett.106.067004 · Physical Review Letters
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Abstract
We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.
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