Critical and in the highly frustrated regime also dynamical properties of the $J_1-J_2$ Ising model with competing nearest-neighbor $J_1$ and second-nearest-neighbor $J_2$ interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within $R\equiv J_2/|J_1|\in [-1/4,0]$. It is confirmed that at least for $R\ge -0.2$ the transition remains second-order and complies with the standard Ising universality class. In the highly frustrated regime of $R<-0.2$ and low temperatures the system tends to freeze to metastable domain states, separated by large energy barriers, which show extremely sluggish dynamics. The resulting huge equilibration and autocorrelation times hinder the analysis of critical properties and thus the character of the transition in this region remains to be determined.

关键的和高度沮丧的政权也具有动力特性。 ${Ĵ}_{\mathrm{1个}}-{Ĵ}_{\mathrm{2个}}$ 具有最近邻竞争性的Ising模型 ${Ĵ}_{\mathrm{1个}}$ 和第二近邻 ${Ĵ}_{\mathrm{2个}}$通过标准的蒙特卡洛（Monte Carlo）和平行回火模拟研究了蜂窝状晶格上的相互作用。确定相界作为在内部顺磁和铁磁状态之间相变的耦合比的函数$\mathrm{[R}\equiv {Ĵ}_{\mathrm{2个}}/|{Ĵ}_{\mathrm{1个}}|\in [-\mathrm{1个}/4，0]$。确认至少$\mathrm{[R}\ge -0.2$过渡仍然是二阶的，并且符合标准的Ising通用性类别。在极度沮丧的政权中$\mathrm{[R}<-0.2$在低温下，系统趋向于冻结到亚稳态的域状态，并被大的能垒隔开，这显示出极其缓慢的动态。所产生的巨大平衡时间和自相关时间阻碍了关键特性的分析，因此该区域中跃迁的特征尚待确定。