振动颗粒系统的非平衡态相变

振动颗粒的分布随着外界驱动的变化会由对称态转为非对称态,即产生对称破缺现象.采用Urn模型,结合Eggers提出的urn的温度与粒子数呈T∝N-2的关系来分析该现象.通过研究细致平衡方程和粒子的概率分布函数获得各条临界线,由此确定相图,并说明了各相的特点.研究了序参量｜ε｜和磁化系数κ在临界线a附近的变化,发现与铁磁-顺磁相变类似;且这两个量的临界行为都满足标度律特点,由此确定临界线a为连续相变线.序参量｜ε｜在变化过程中会出现磁滞现象,由此确定临界线c为一级相变线.讨论发现这些相变现象的产生源自温度函数与urn模型本身的动力学行为.

Non-Equilibrium Phase Transition of Shaken Particles

The distribution of shaken particles changes with the external driven from the symmetric state to the non-symmetric state,resulting in the symmetry breaking. A model is introduced to analyze this phe- nomenon,combining with the relationship of T∝ N-2 between temperature and the number of particles proposed by Eggers. Each critical line is obtained and the phase transition diagram is given, and the characteristics of each phase are described by studying the detailed balance equation and the probability distribution function. The behaviors of the order parameter ｜ε｜ and the susceptibility K are found to be close to the critical line, which is similar to that of the ferromagnetie-paramagnetic transition. The critical behaviors have the features of the scaling law. It is found that the line a is a continuous phase transition line. The hysteresis phenomenon appears during the changing procedure of the order parameter ｜ε｜, which decides the critical line c as the first order phase transition line. The analyses show that the phase transition phenomenon originates from the temperature function and the dynamical behavior of urn model itself.