Dynamics for spherical spin glasses: Gibbs distributed initial conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913790571839488 |
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| author | Dembo, Amir Subag, Eliran |
| author_facet | Dembo, Amir Subag, Eliran |
| contents | We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperature $T$, for spherical mixed $p$-spin disordered mean-field models, initialized according to a Gibbs measure for temperature $T_0$, in the replica-symmetric (RS) or $1$-replica-symmetry-breaking (RSB) phase. For any $T_0=T$ above the dynamical phase transition point $T_c^{\rm dyn}$ the resulting stationary relaxation dynamics coincide with the FDT solution for these equations, while for lower $T_0=T$ in the $1$-RSB phase, the relaxation dynamics coincides with the FDT solution, now concentrated on the single spherical band within the Gibbs measure's support on which the initial point lies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics for spherical spin glasses: Gibbs distributed initial conditions Dembo, Amir Subag, Eliran Probability We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperature $T$, for spherical mixed $p$-spin disordered mean-field models, initialized according to a Gibbs measure for temperature $T_0$, in the replica-symmetric (RS) or $1$-replica-symmetry-breaking (RSB) phase. For any $T_0=T$ above the dynamical phase transition point $T_c^{\rm dyn}$ the resulting stationary relaxation dynamics coincide with the FDT solution for these equations, while for lower $T_0=T$ in the $1$-RSB phase, the relaxation dynamics coincides with the FDT solution, now concentrated on the single spherical band within the Gibbs measure's support on which the initial point lies. |
| title | Dynamics for spherical spin glasses: Gibbs distributed initial conditions |
| topic | Probability |
| url | https://arxiv.org/abs/2503.23342 |