Ising models with frustrated next-nearest-neighbor interactions present a rich array of modulated phases. These phases however assemble and relax slowly which hinders their computational study. In two dimensions strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method which bypasses both difficulties can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau Phys. Rev. B 103 094441 (2021)] in which we evaluated the two-dimensional axial next-nearest-neighbor Ising (ANNNI) model with transfer matrices we here extend the effective usage of the TM method to Ising models with biaxial diagonal and third-nearest-neighbor frustration (BNNNI DNNI and 3NNI models). The high-accuracy TM numerics help resolve various physical ambiguities about these reference models thus providing a clearer overview of modulated phase formation in two dimensions.
