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arXiv · 1009.2551

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

Rafael M. Fernandes·Jörg Schmalian
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Abstract

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2πρ$. For irrational $ρ$, 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.

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Rafael M. Fernandes, Jörg Schmalian. 2011-01-19. Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons. https://doi.org/10.1103/physrevlett.106.067004

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