The low-lying energy spectrum of a spinning quantum chain in the critical region is calculated by using Lanczos method. According to conformal theory, the anomalous dimensions ? and the normalising factor ? are obtained from the energy spectrum. Also a simple derivation of the field theory of the model is given.
Finite-Size-Scaling and Conformal Invariance are used in order to find the phase diagram and critical exponents of a quantum spin chain with spin S=3/2. The model has a tetracritical point besides critical lines. The conformal anomaly and anomalous dimensions of some primary operators are calculated at the tetracritical point.