【摘 要】
：
It has been widely discussed whether long-range magnet-ic order could exist in low-dimensional (d ＜ 3) systems.Early studies,like Hohenberg-Mermin-Wagner theorem based on the Heisenberg model of magnetism,incline to a negative con-clusion,as the thermal f
【机 构】
：
Beijing Academy of Quantum Information Sciences,Beijing 100193,China
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It has been widely discussed whether long-range magnet-ic order could exist in low-dimensional (d ＜ 3) systems.Early studies,like Hohenberg-Mermin-Wagner theorem based on the Heisenberg model of magnetism,incline to a negative con-clusion,as the thermal fluctuation at any finite temperature prevents the formation of long-range magnetic order[1,2].However,further studies theoretically predicted an unusual long-range magnetic order in the two-dimensional (2D) sys-tems that are described by a so-called 2D-XY model,result-ing from the formation of bound pairs of vortices and anti-vor-tices with opposite chirality[3,4].The induced ferromagnetism is suppressed as the 2D system is heated over a critical temper-ature,accompanied with the destruction of those bound pairs and thus the long-range magnetic order.This mechan-ism of phase transition is known as Berezinskii-Kosterlitz-Thou-less (BKT) formalism[3-5].
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