Ising model with competing axial interactions in the presence of a field: A renormalization-group treatment

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Abstract
On the basis of an ε expansion, we present a renormalization-group analysis of the anisotropic next-nearest-neighbor Ising model in a field. For small fields, the γ surface remains XY-like. For larger fields, we confirm the existence of lines of tricritical points which are governed by Gaussian-type exponents. We pay special attention to the many couplings between a two-component critical spin field, associated with the main harmonic component of the magnetization, and several noncritical spin fields, associated with the uniform and the higher harmonic components. We remark that it is necessary to take into account the uniform and the second-harmonic components of the magnetization to describe the tricritical behavior.