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• W3105909120 startingPage "P09018" @default.
• W3105909120 abstract "We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical exponents characterising this phase transition are computed analytically and compared with those of the corresponding $D$-dimensional short-range model, leading to conclude that the usual mapping between one dimensional long-range models and $D$-dimensional short-range models holds exactly for this system, in contrast to models with Ising spins. Moreover, the critical exponents of the pure model and those of the random field model satisfy a relationship that mimics the dimensional reduction rule. The absence of a spin-glass phase is strongly supported by the local stability analysis of the replica symmetric saddle-point as well as by an independent computation of the free-energy using a renormalization-like approach. This latter result enlarges the class of random field models for which the spin-glass phase has been recently ruled out." @default.
• W3105909120 created "2020-11-23" @default.
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• W3105909120 date "2014-09-16" @default.
• W3105909120 modified "2023-10-14" @default.
• W3105909120 title "Statistical mechanics of the spherical hierarchical model with random fields" @default.
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• W3105909120 doi "https://doi.org/10.1088/1742-5468/2014/09/p09018" @default.
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