As a simplified model of randomly pinned vortex lattices or charge-densitywaves, we study the random-field XY model on square ($d=2$) and simple cubic($d=3$) lattices. We verify in Monte Carlo simulations, that the averagespacing between topological defects (vortices) diverges more strongly than theImry-Ma pinning length as the random field strength, $H$, is reduced. Wesuggest that for $d=3$ the simulation data are consistent with a topologicalphase transition at a nonzero critical field, $H_c$, to a pinned phase that isdefect-free at large length-scales. We also discuss the connection between thepossible existence of this phase transition in the random-field XY model andthe magnetic field driven transition from pinned vortex lattice to vortex glassin weakly disordered type-II superconductors.
展开▼
机译：作为随机固定的涡旋晶格或电荷密度波的简化模型，我们研究了正方形（$ d = 2 $）和简单三次方（$ d = 3 $）晶格上的随机场XY模型。我们在蒙特卡洛模拟中验证，随着随机场强度$ H $的减小，拓扑缺陷（涡旋）之间的平均间距比艾玛-马宁钉扎长度的差异更大。我们建议，对于$ d = 3 $，模拟数据与非零临界场$ H_c $到固定长度的无缺陷固定相的拓扑相变一致。我们还讨论了在弱场Ⅱ型超导体中，随机场XY模型中可能存在这种相变与磁场驱动的从固定涡旋晶格到涡旋玻璃的跃迁之间的联系。
展开▼
