Statics and Dynamics of Metastability

Abstract

Metastability in the system with short-range forces is discussed from unified viewpoints of statics and dynamics. The system-size dependence of the double-minimum free-energy is argued after exact calculations with a spherical model. A coercive field is defined by statics, which agrees with that of the critical droplet theory and characterizes super-critical or sub­ critical situations. In dynamics a long-wavelength cutoff theory is applied to finite systems. A coercive field for a finite system is also defined by this dynamics, which just agrees with that defined by statics. It is shown that the mechanism of the decay process of metastable states is an instability of the long-range spatial fluctuation in the super-critical region and is a stochastic barrier penetration in the sub-critical region. Results are compared with computer experiments on finite systems. § l. Introduction As is seen in the conventional critical-droplet theory by Becker and Doring/> the decay process of the metastable states is the problem of instability of the long-range spatial fluctuations. Especially in the systems with short-range forces the roles of spatial fluctuations seem to be very significant. We have recently proposed a mean spherical approximation2>.s> for the nonlinear couplings of fluctua­ tions by using stochastic TDGL model proposed by Langer, - 5> and have shown the metastable behaviours to appear both in the quenched and in the field-in­ verted spin systems. A remarkable nature is the transient, unstable growth of the long-range fluctuations, which can be generally expected from viewpoints of a sum-rule for the fluctuation spectrum and the local equilibrium assumption. The purpose of the present work is to make this fluctuation picture clearer by considering finite systems, where some modes of long-range fluctuations should be cut off. From a static viewpoint the metastability in systems with short-range forces was investigated by calculating a double-minimum free-energy of finite-system, 6> but compared with systems with weak, long-range forces 7>.s> there have been few works on the unified understandings from static and dynamic viewpoints. 9> An unified picture is expected to reply to some questions on the singularity in the limit of infinite systems, e.g., the stability of the spontaneously magnetized state of a spin system in spite of the flatness of the free-energy. Of course we have questions on the finite system itself. For example, computer experiments/okJal which are very powerful in the investigation of the dynamical phenomena, are