# Spherical Spin Glass Model with External Field

@article{Baik2020SphericalSG,
title={Spherical Spin Glass Model with External Field},
author={Jinho Baik and Elizabeth Collins-Woodfin and Pierre le Doussal and Hao Wu},
journal={arXiv: Disordered Systems and Neural Networks},
year={2020}
}
• Published 13 October 2020
• Physics
• arXiv: Disordered Systems and Neural Networks
We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes to zero as the dimension of the spin variable grows. In particular, we consider overlaps with the…
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## References

SHOWING 1-10 OF 47 REFERENCES
Overlaps of a spherical spin glass model with microscopic external field
We examine the behavior of the 2-spin spherical Sherrington-Kirkpatrick model with an external ﬁeld by analyzing the overlap of a spin with the external ﬁeld. Previ-ous research has noted that, at
Fluctuations of the free energy in the mixed p-spin models with external field
• Mathematics
• 2015
We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the
The Thermodynamic Limit in Mean Field Spin Glass Models
• Mathematics
• 2002
Abstract: We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as
On the overlap in the multiple spherical SK models
• Mathematics
• 2007
In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the
Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction
• Mathematics, Physics
• 2016
We consider a spherical spin system with pure 2-spin spherical Sherrington–Kirkpatrick Hamiltonian with ferromagnetic Curie–Weiss interaction. The system shows a two-dimensional phase transition with
The sphericalp-spin interaction spin glass model: the statics
• Physics
• 1992
The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step
Parisi Formula, Disorder Chaos and Fluctuation for the Ground State Energy in the Spherical Mixed p-Spin Models
• Physics
• 2015
We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for
Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field
We prove the existence of a critical regime of fluctuation of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field. Such regime was conjectured in [2,12], and
Fluctuations of the overlap at low temperature in the 2-spin spherical SK model
• Mathematics
• 2019
We describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order
Some comments on the Sherrington-Kirkpatrick model of spin glasses
• Physics
• 1987
In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated