New Universality Classes in 1D O(N)-Invariant Spin-Models with an n-Parametric Action

Abstract

An action with n parameters (couplings), which generalizes the mixed O(N)-RP ^N−1-model, is considered in one dimension for general N. The non-negativity of the parameters ensures that the transfer matrix is a positive operator due to reflection positivity and therefore allows a quantum-mechanical interpretation of the spectrum. Using 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 behaviour determines a one-parameter family of new universality classes. Reflecting the true spectral properties of the transfer matrix, they interpolate between the classes of the O(N)-vector-model and the RP ^N−1-model. Furthermore continuum limits are discussed, including the exceptional case N = 2.