Staniscia F, Chavanis P H, De Ninno G, Fanelli D
Dipartimento di Fisica, Università di Trieste, 34127 Trieste, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):021138. doi: 10.1103/PhysRevE.80.021138. Epub 2009 Aug 31.
Systems with long-range interactions display a short-time relaxation toward quasistationary states (QSSs) whose lifetime increases with system size. The application of Lynden-Bell's theory of "violent relaxation" to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first- and second-order phase transitions between homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct N -body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bell's theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find unmagnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region. We also report the existence of a region with negative specific heats for QSSs both in the numerical and analytical caloric curves.
具有长程相互作用的系统会朝着准稳态（QSSs）呈现出短时间弛豫，其寿命随系统规模增加。将林登 - 贝尔的“剧烈弛豫”理论应用于哈密顿平均场模型，可预测在均匀（零磁化强度）和非均匀（非零磁化强度）准稳态之间存在非平衡一阶和二阶相变，以及一个有趣的相重入现象。我们将这些理论预测与直接的N体数值模拟进行比较。我们证实了在林登 - 贝尔理论预测的典型参数范围内存在相重入，但同时也表明情况比最初设想的更为复杂。特别是，我们展示了次级重入相的存在：我们在理论上的磁化区域中发现了未磁化状态，以及在理论上的未磁化区域中存在持续的磁化状态。我们还报告了在数值和解析热容量曲线中，准稳态都存在具有负比热容的区域。
