二维ANNNI模型的Kosterlitz无相变
Kosterlitz-Thouless Phase Transition of the ANNNI model in Two Dimensions
摘要：
二维轴向次近邻伊辛（ANNNI）模型的自旋结构是一个新的问题，不同的蒙特卡罗（MC）模拟方法预测的自旋序不同.通常的平衡模拟预测发生浮动无公度（IC）Kosterlitz无公度（KT）型相，这从来没有出现在非平衡弛豫（NER）模拟。在本文中，我们首先检查先前发表的结果，这两种方法，然后调查一个较高的转变温度，$T_{c1}$，IC和顺磁相之间。在通常的平衡模拟中，我们计算较大晶格上的层磁化（直到$512 \times 512$位置），并使用阻挫比$κ(\equiv -J_2/J_1) = 0.6$估计$T_{c1} \approx 1.16J$。我们研究的相变的自旋重叠函数的Binder比$g_L$和相关长度比$ξ/L$的性质。在NER模拟中，我们通过自相关函数观察到平衡态的自旋动力学，并且还观察到从基态和无序态的层磁化弛豫。这些量在$T \lesssim 1.17J$处表现出代数衰减。我们的结论是，二维ANNNI模型实际上承认的IC相变的KT型。
英文摘要：
The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature, $T_{c1}$, between the IC and paramagnetic phases. In the usual equilibrium simulation, we calculate the layer magnetization on larger lattices (up to $512 \times 512$ sites) and estimate $T_{c1} \approx 1.16J$ with frustration ratio $κ(\equiv -J_2/J_1) = 0.6$. We examine the nature of the phase transition in terms of the Binder ratio $g_L$ of spin overlap functions and the correlation-length ratio $ξ/L$. In the NER simulation, we observe the spin dynamics in equilibrium states by means of an autocorrelation function, and also observe the layer magnetization relaxations from the ground and disordered states. These quantities exhibit an algebraic decay at $T \lesssim 1.17J$. We conclude that the two-dimensional ANNNI model actually admits an IC phase transition of the KT type.
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