The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain $\left(J\right)$ and interchain nearest-neighbor $\left(J_1\right)$ and next-nearest-neighbor $\left(J_2\right)$ interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at $J_2=-J_1/2$ for a rectangular lattice and $J_2=-J_1$ for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

• Received 22 October 2016

DOI:https://doi.org/10.1103/PhysRevE.94.062134