Critical properties of random and constrained dipolar magnets

Renormalization-group techniques are used to study a model of n-coupled m-component spin systems, in the limit of large dipole-dipole interactions. As recently shown by Emery, this model describes the critical behavior of a constrained dipolar system in the limit n→ and that of a dipolar system with a quenched random perturbation in the limit n→0. In both cases, the unperturbed dipolar fixed point is unstable, and there is a crossover to a new behavior. For the constrained system, this leads to another dipolar fixed point (if α<0, α being the dipolar specific-heat exponent) with the same thermodynamic critical exponents, or to one with renormalized dipolar exponents (if α>0). These results are different from those of previous "spherical" dipolar models. For the random case, the crossover is either to a new fixed point, with very different exponents, e.g., 2 ν1+1.183ε for m=d=4-ε, or away from all the fixed points found to order ε. One of the new fixed points in this case has complex eigenvalues of the linearized recursion relations. This is related to the fact that the recursion-relation flow is not of a gradient type for random systems.