Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.
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2017-05-26
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Abstract
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d<d_{u} using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.
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Charbonneau, Patrick, and Sho Yaida (2017). Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions. Phys Rev Lett, 118(21). p. 215701. 10.1103/PhysRevLett.118.215701 Retrieved from https://hdl.handle.net/10161/15346.
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Patrick Charbonneau
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