Topological Charge Distribution and $C{P}^1$ Model with $\hat{I}¸$ Term

Abstract

The two dimensional $C{P}^1$ model with $\hat{I}¸$ term is simulated. We compute the topological charge distribution $P(Q)$ by employing the ``set method" and ``trial function method", which are effective in the calculations for very wide range of $Q$ and large volume. The distribution $P(Q)$ shows the Gaussian behavior in the small ${\hat{I}}^2$ (inverse coupling constant) region and deviates from it in the large ${\hat{I}}^2$ region. The free energy and its moment are calculated as a function of $\hat{I}¸$. For small ${\hat{I}}^2$, the partition function is given by the elliptic theta function, and the distribution of its zeros on the complex $\hat{I}¸$ plane leads to the first order phase transition at $\hat{I}¸=\ddot{I}€$. In the large ${\hat{I}}^2$ region, on the other hand, this first order phase transition disappears, but definite conclusion concerning the transition is not reached due to large errors.

22 pages, plaintex, one table, seven figures