The Monte Carlo simulation of 2D ANNNI-model

In this, study we present the data for 2D Axial Next Nearest Neighbor Ising model (ANNNI-model) obtained from Monte Carlo (MC) simulations using the standard Metropolis algorithm. The temperature dependences of thermodynamic parameters for a cubic lattice with linear sizes L=32 at different values of the competing interaction parameter |J1/J|=0.1÷1.0. Transition temperatures of ferromagnetic ordering to the paramagnetic state at |J1/J|<0.3 and to the modulated state at 0.3<|J1/J|<0.5 are shown to shift towards low temperatures with an increase in a competing interaction parameter absolute value. Conversely, transition temperatures of the modulate state to the paramagnetic ordering grow. The modulated ordering in the 2D ANNNImodel appears in the temperature range 0.1<T<2.0 at 0.2<|J1/J|≤1.0. Modulated structure parameters are computed using a mathematic apparatus of Fourier transform spectral analysis. According to the Fourier analysis results, the wave number grows with an increase in the competing interaction parameter absolute value. Summarizing obtained results, we plot a phase diagram of 2D anisotropic Ising model with competing interactions.