Shun Ogawa, Aurelio Patelli, Yoshiyuki Y. Yamaguchi
The critical exponent of susceptibility is expected as 1 in systems belonging to the mean-field universality class. On the other hand, the mean-field nature permits to introduce the Vlasov equation in the place of the Liouville equation, and the linear response theory based on the Vlasov equation gives the strange exponent 1/4 in the low-temperature side of the Hamiltonian mean-field model. We clarify that this strange exponent is due to existence of Casimir invariants which traps the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by N-body simulations and numerical Vlasov solutions.
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http://arxiv.org/abs/1304.2982
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