The phase transitions of frustrated J_1-J_2 Ising model on the honeycomb lattice

We study the two-dimensional (2D) frustrated J_1-J_2 Ising model on the 

honeycomb lattice using Monte Carlo calculations. Here J_1 < 0 and J_2 > 0

are the nearest and the next-to-nearest couplings. The observables

computed include the magnetization, the susceptibility, the energy density,

and the specific heat. Based on careful finite-size analyses, we conclude

that the phase transitions for J_2/|J_1| = 0.2, 0.22, 0.23, and 0.24

are second order and are governed by the 2D Ising universality class.

Moreover, our results convincingly imply that there are likely phase 

transitions for J_2/|J_1| = 1.0, 0.8, and 0.5. For J_2/|J_1| = 0.3, our 

numerical data favor the scenario that no phase transition occurs for 

this value of J_2/|J_1|. Due to the abnormal large integrated autocorrelation 

times, we are not able to obtain any information regarding the critical 

phenomena of 0.24 < J_2/|J_1| < 0.3.