Exactly solvable model exhibiting a multicritical point

A hypercubic d-dimensional lattice of spins with nearest neighbor ferromagnetic coupling and next nearest neighbor antiferromagnetic coupling along a single axis is studied in the spherical model limit (n→∞) and is found to exhibit a multicritical point of the uniaxial Lifshitz type. The shape of the λ line is calculated explicitly in the vicinity of the multicritical point, and analytic expressions are given for the shift exponent ψ(d) and its amplitudes A±(d). The amplitude A_(d) changes sign for d = 3.