Multicomponent field theories and classical rotators

It is shown that a D-component Euclidean quantum field, φ{symbol}=(φ{symbol}¹,...,φ{symbol}^D), with λ|φ{symbol}|⁴+β|φ{symbol}²| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the case D=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies for D=2 or 3 and that Griffiths' second inequality is valid for D=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality for D=2, an interesting relation between the "parallel" and "transverse" two-point correlations is obtained.