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

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

1996-09-16

arxiv.org/abs/hep-lat/9609030v1

J.Math.Phys. 38 (1997) 4872-4881

Physics

High Energy Physics

High Energy Physics - Lattice

13 pages

Scientific paper

10.1063/1.532131

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 $N=2$.

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