New Universality Classes in One--Dimensional $O(N)$--Invariant Spin--Models with an $n$--Parametric Action

Abstract

An action with $n$ parameters, which generalizes the $O(N)-R{P}^{N-1}$ -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 behaviour determines a one-parameter family of new universality classes. They interpolate between the $O(N)$-vector-model-class and the $R{P}^{N-1}$-model-class. Furthermore continuum limits are discussed, including the exceptional case $N=2$.

13 pages

References in corpus (1)

• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models

Cited by in corpus (3)

• Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models
• More on coupling coefficients for the most degenerate representations of SO(n)
• Gauged O(n) spin models in one dimension