Balakrishnan R, Mehta M
The Institute of Mathematical Sciences, CIT Campus, Chennai 600 113, India.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1312-9. doi: 10.1103/physreve.61.1312.
We study the lowest-lying excitation of a classical ferromagnetic XY spin chain, in the presence of a symmetry breaking magnetic field. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allowed phase space shrinks with increasing field in a nontrivial manner. The orbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find the lowest energy among them, excluding the obvious ground state configuration with all spins parallel along the field direction. This state turns out to be the unstable fixed point of the map. We show that up to a certain (primary) critical field, a separatrixlike 2pi soliton configuration is the lowest-energy excitation, with an energy very close to the ground state energy. For any field beyond this critical field, the soliton disappears and lowest excitation is a librational configuration corresponding to the outermost orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the difference in energy between the former and the latter at this field. With further increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex behavior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.
我们研究了在存在对称破缺磁场的情况下经典铁磁XY自旋链的最低激发态。使该系统的能量取极值会得到一个二维非线性映射，其允许的相空间会以一种非平凡的方式随着磁场增加而收缩。该映射的轨道代表了极值能量自旋构型的集合。对于每个磁场，我们计算该集合中成员的能量，并找出其中的最低能量，但不包括所有自旋都沿磁场方向平行排列的明显基态构型。结果表明，这个态是映射的不稳定不动点。我们表明，直到某个（主要）临界磁场，一种类似分界线的2π孤子构型是最低能量激发态，其能量非常接近基态能量。对于超过这个临界磁场的任何磁场，孤子消失，最低激发态是一种振动构型，对应于该磁场下相图中的最外轨道。此外，我们发现其能量远高于基态能量，导致在该磁场下前者与后者之间的能量差出现急剧跃升。随着磁场进一步增加，在某些次要临界磁场处激发能量也会出现急剧跃升。我们表明，当相应的自旋构型变得可公度时，这些跃升就会出现。我们对这种复杂的能量行为进行了解释，并研究了其对系统磁化强度和静态磁化率的影响。
