Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.
Phys Rev E. 2017 May;95(5-1):052150. doi: 10.1103/PhysRevE.95.052150. Epub 2017 May 30.
We consider the zero-temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighborhood. The Hamiltonian is given by H=-∑{〈i,j〉}S{i}S_{j}-κ∑{〈i,j^{'}〉}S{i}S_{j^{'}}, where the two terms are for the first neighbors and second neighbors, respectively, and κ≥0. The freezing phenomenon, already noted in two dimensions for κ=0, is seen to be present for any κ. However, the frozen states show more complicated structure as κ is increased; e.g., local antiferromagnetic motifs can exist for κ>2. Finite-sized systems also show the existence of an isoenergetic active phase for κ>2, which vanishes in the thermodynamic limit. The persistence probability shows universal behavior for κ>0; however, it is clearly different from the κ=0 results when a nonhomogeneous initial condition is considered. Exit probability shows universal behavior for all κ≥0. The results are compared with other models in two dimensions having interactions beyond the first neighbor.
我们考虑二维伊辛模型在零温下的粗化，其中自旋在摩尔邻域内相互作用。哈密顿量为 H=-∑{〈i,j〉}S{i}S_{j}-κ∑{〈i,j^{'}〉}S{i}S_{j^{'}}，其中前一项是近邻相互作用，后一项是次近邻相互作用，κ≥0。在二维情况下，对于 κ=0，已经观察到冻结现象，对于任何 κ 都存在。然而，随着 κ 的增加，冻结态表现出更复杂的结构；例如，对于 κ>2，可以存在局部反铁磁图案。有限大小的系统也显示出对于 κ>2 存在等能量活跃相，在热力学极限下消失。对于 κ>0，持续概率表现出普遍行为；然而，当考虑非均匀初始条件时，它与 κ=0 的结果明显不同。退出概率对于所有 κ≥0 都表现出普遍行为。将结果与二维中具有超过近邻相互作用的其他模型进行了比较。
