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

## TL;DR

This paper introduces a family of new universality classes in one-dimensional $O(N)$-invariant spin models with an $n$-parameter action, expanding understanding of critical behavior and continuum limits in these models.

## Contribution

It generalizes existing models by identifying a family of hypersurfaces that define new universality classes interpolating between known models.

## Key findings

- Identification of critical hypersurfaces for the models.
- Existence of a one-parameter family of universality classes.
- Discussion of continuum limits, including special case N=2.

## 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 $N=2$.