Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-$p$-spin model in a self-induced field

Abstract

We report some results on the quenched disordered Spherical multi-$p$-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous-amorphous transitions and spin-glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information.

34 pages, 7 figures

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• General phase-diagram of multimodal ordered and disordered lasers in closed and open cavities
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• The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra
• The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media
• Statistical mechanics models for multimode lasers and random lasers
• Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference
• Replica Fourier Transform: Properties and Applications
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Intensity pseudo-localized phase in the glassy random laser