Relaxation and overlap probability function in the spherical and mean spherical model

Abstract

The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to below the critical temperature. It is found that there exists a crossover time $t^{\ast }\sim V^{2/d}$ such that for $t<t^{\ast }$ the two models are equivalent, while for $t>t^{\ast }$ macroscopic discrepancies arise. The relation between the off equilibrium response function and the structure of the equilibrium state, which usually holds for phase ordering systems, is found to hold for the spherical model but not for the mean spherical one. The latter model offers an explicit example of a system which is not stochastically stable.

11 pages, 1 figure, references corrected, to appear in Phys.Rev.E

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Cited by in corpus (22)

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• Fluctuation-Dissipation relations far from Equilibrium
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• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Heat exchanges in a quenched ferromagnet
• Spherical model of growing interfaces
• Kinetics of the long-range spherical model
• Lindblad dynamics of a quantum spherical spin
• The kinetic spherical model in a magnetic field
• Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
• Lindblad dynamics of the quantum spherical model
• Axiomatic construction of quantum Langevin equations
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• The role of initial conditions in the ageing of the long-range spherical model
• Non-equilibrium relaxations: ageing and finite-size effects
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Kinetics of phase-separation in the critical spherical model and local scale-invariance
• Condensation of Fluctuations in the Ising Model: a Transition without Spontaneous Symmetry Breaking
• Non trivial behavior of the linear response function in phase ordering kinetics
• Relation between Statics and Dynamics in the Quench of the Ising Model to below the Critical Point
• Self tuning phase separation in a model with competing interactions inspired by biological cell polarization