Yamaguchi Yoshiyuki Y
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Sep;92(3):032109. doi: 10.1103/PhysRevE.92.032109. Epub 2015 Sep 8.
We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions.
我们研究了哈密顿平均场模型中对外部磁场的响应，该模型是铁磁体的一个典型玩具模型，由诸如XY自旋的平面转子组成。由于长程相互作用，外部场在系统达到热平衡之前将其驱动到一个持久的准稳态，并且基于弗拉索夫方程的线性响应理论预测了在准稳态下获得的磁化率张量。对于空间均匀的稳定状态，其动量分布不对称且均值为0，该理论表明，对于渐近恒定的外部场，磁化率张量既不对称也不可对角化，因此预测的状态不是静止的。此外，即使在稳定性阈值处，该张量也没有散度。这些理论发现通过对斜正态分布函数的弗拉索夫方程进行直接数值模拟得到了证实。
