Critical point of a para-ferrimagnetic phase transition of the ANNNI model in a field

The finite field para-ferrimagnetic phase transition in the axial next-nearest-neighbor Ising (ANNNI) model is studied by using the linear perturbation real space renormalization group transformation. The method is examined in systems of ferromagnetic and antiferromagnetic Ising chains coupled by ferromagnetic interactions in the longitudinal field. As one would expect, the external field in the first case destroys the continuous phase transition and in the second shifts the critical point toward a lower temperature according to the square law. For the ferromagnetic chains coupled by the competing interchain nearest-neighbor J(1) < 0 and next-nearest-neighbor J(2) < 0 interactions, the external field changes the character of the phase transition from continuous to discontinuous. However, it has been found that for the ratio J(2)/J(1) around 0.5 there is a critical value of the field for which an isolated critical point exists. The temperature dependences of the specific heat for several values of J(2)/J(1) and the external field are presented.