正方形晶格在外部场中的海德模型
Heider balance in square versus triangular lattices under an external field
AI总结：
本文研究了外部场对正方形晶格海德模型的影响，通过三种方法推导了系统边磁化磁滞系数的精确表达式。
摘要：
我们讨论了在外部社会场作用下海德模型的情况。该场被引入以打破敌对关系和友好关系概率之间的对称性。我们考虑了在热噪声产生的波动作用下系统的状态，并展示了对二维三角形和正方形网络（具有周期性边界条件）的比较研究结果。结果通过三种不同方法获得：对小系统进行精确计算，对中等规模系统进行蒙特卡罗模拟，以及在热力学极限下（对应于无限大小）对某些可解析求解的极限情况的精确计算。特别是，我们利用最近发现的结构平衡系统与伊辛模型之间的等价性，推导出处于海德平衡状态的系统边磁化磁滞系数的精确形式。
英文摘要：
We discuss the Heider model in the presence of an external social field. This field breaks the possible symmetry between the probabilities of hostile and friendly relationships. We consider the system in the presence of fluctuations generated by thermal noise and present the results of a comparative study of two-dimensional triangular and square networks with periodic boundary conditions. The results were obtained using three different methods: exact calculations for small systems ($3 \times 3$ square lattice and $2 \times 2$ triangular lattice), Monte Carlo simulations of medium-sized systems ($16 \times 16$ lattices), and exact calculations in the thermodynamic limit (corresponding to infinite size) of certain limiting cases for which analytical solutions are possible. In particular, we exploit the recently discovered equivalence between structurally balanced systems and the Ising model to derive an exact form of the edge magnetization susceptibility for systems in Heider equilibrium.
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