Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
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| Format: | Preprint |
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2023
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| _version_ | 1866911885290373120 |
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| author | Machado, David Mulet, Roberto Ricci-Tersenghi, Federico |
| author_facet | Machado, David Mulet, Roberto Ricci-Tersenghi, Federico |
| contents | We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the continuous-time relaxation of the system, that translates into a set of differential equations for the evolution of local probabilities. The solution to these dynamical mean-field equations describes very well the out-of-equilibrium dynamics at high temperatures, notwithstanding the key observation that the off-equilibrium probability measure contains higher-order interaction terms, not present in the equilibrium measure. In the low-temperature regime, the solution to the dynamical mean-field equations shows the correct two-step relaxation (a typical feature of the glassy dynamics), but with a relaxation timescale too short. We propose a solution to this problem by identifying the range of energies where entropic barriers play a key role and defining a renormalized microscopic timescale for the dynamical mean-field solution. The final result perfectly matches the complex out-of-equilibrium dynamics computed through extensive Monte Carlo simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_00882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures Machado, David Mulet, Roberto Ricci-Tersenghi, Federico Statistical Mechanics We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the continuous-time relaxation of the system, that translates into a set of differential equations for the evolution of local probabilities. The solution to these dynamical mean-field equations describes very well the out-of-equilibrium dynamics at high temperatures, notwithstanding the key observation that the off-equilibrium probability measure contains higher-order interaction terms, not present in the equilibrium measure. In the low-temperature regime, the solution to the dynamical mean-field equations shows the correct two-step relaxation (a typical feature of the glassy dynamics), but with a relaxation timescale too short. We propose a solution to this problem by identifying the range of energies where entropic barriers play a key role and defining a renormalized microscopic timescale for the dynamical mean-field solution. The final result perfectly matches the complex out-of-equilibrium dynamics computed through extensive Monte Carlo simulations. |
| title | Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2307.00882 |