The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited

Abstract

Simulational studies of spin glasses in the last decade have focussed on the so-called replicon exponent $\alpha$ as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking picture of Parisi or by the droplet-scaling picture. On the latter picture, it should be zero, but we shall argue that it will only be zero for systems of linear dimension $L>L^{\ast }$. The crossover length $L^{\ast }$ may be of the order of hundreds of lattice spacings in three dimensions and approach infinity in 6 dimensions. We use the droplet-scaling picture to show that the apparent non-zero value of $\alpha$ when $L<L^{\ast }$ should be $2\theta$, where $\theta$ is the domain wall energy scaling exponent, This formula is in reasonable agreement with the reported values of $\alpha$.

arXiv comment8 pages, 1 figure. Final version. Extra references added, plus a discussion of equilibration and the de Almeida-Thouless line

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• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
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• Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization
• q-Gaussian Crossover in Overlap Spectra towards 3D Edwards-Anderson Criticality