New universality classes in one-dimensional O(N)-invariant spin-models with an n-parametric action

An action with n parameters, which generalizes the O(N)-RPN-1 model, is considered in one dimension for general N. We use asymptotic expansion techniques to determine where the model becomes critical and show that for the actions considered there exists a family of hypersurfaces whose asymptotic behavior determines a one-parameter family of new universality classes. They interpolate between the O(N) vector model class and the RPN-1 model class. Furthermore continuum limits are discussed, including the exceptional case N=2. copyright 1997 American Institute of Physics