Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature |
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| Authors: | Amir Dembo Alice Guionnet Christian Mazza |
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| Affiliation: | (1) Department of Statistics, Stanford University, Stanford, CA 94305, USA;(2) Department of Mathematics, Stanford University, Stanford, CA 94305, USA;(3) UMPA, Ecole Normale Superieure de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France;(4) Département de Mathématiques, Université Pérolles, Chemin du Musée 23, CH-1700 Fribourg, Suisse |
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| Abstract: | We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. We provide a mathematically rigorous derivation of their FDT solution (for the high temperature regime) and of certain key properties of this solution, which are in agreement with earlier derivations based on physical grounds. AMS (2000) Subject Classification: Primary: 82C44 Secondary: 82C31, 60H10, 60F15, 60K35 |
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| Keywords: | Interacting random processes disordered systems statistical mechanics Langevin dynamics Aging p-spin models |
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