Colloquium

Phase diagram of Quasi-stationary state in the Hamiltonian mean-field model by Landau's phenomenological theory

Ogawa Shun

12th November (Fri) 13:30

Some kinds of systems with long-range interactions are trapped at quasi-stationary states (QSSs) whose life time diverge with system size. Out-of-equilibrium phase transitions of Hamiltonian-Mean-Field (HMF) model was investigated by A. Antoniazzi et al. [Phys.Rev.Lett.,99,040601]. It has been checked that results of N-body simulations supported for small initial order parameters and large one. However, F. Staniscia et al. [Phys.Rev.E,80,021138] remarked that the difference between N-body simulations and statistical theory appears around ``the tricritical point". They constructed the phase diagram by seeking the maximum point of entropy. This method require solving the complex simultaneous equation. The critical line can be found only pointwise. The accuracy therefore is not so good. So the exact equations to determine critical points and ``the tricritical point" are needed. In this talk, I quickly review Lynden-Bell's statistical theory and introduce the way to construct the pseudo-free-energy based on the Lynden-Bell's pioneering idea and stability criteria of the Vlasov equation. It gives exact equations to determine ``the tricritical point" and the line in which continuous phase transition occurs. The discontinuous transition line and the line in which the metastable solutions appear are constructed approximately with it. This procedure for constructing the phase-diagram is much easier than that done in previous studies. Finally I introduce the N-body simulations around ``the tricritical point".