Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions

Abstract

We investigate response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like the XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasista- tionary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with zero-means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for the skew-normal distribution functions.

10 pages, 8 figures

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Lynden-Bell and Tsallis distributions for the HMF model
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model

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