# Poster presented by Guillermo Palma

**Poster Session**
**Topic:** Improvement and Renormalization

### 1-Loop Improved lattice Action for the Nonlinear Sigma-Model

**Abstract:** Starting from the 2-D nonlinear $\sigma$-Model we compute the Wilson effective action on a lattice of lattice spacing $a^{'}$ in the 1-loop approximation for a choice of blockspin $\Phi (x)=C\phi (x)/\left| C\phi (x)\right| $, where $C$ is averaging of $\phi (z)$ over a block $x$. We use a $\delta $-function constraint to enforce the blockspin definition. The result is composed of the classical perfect action with a renormalized coupling constant $\beta _{eff}$, an augmented contribution from the jacobian, further correction terms depending on fluctuations of $\beta _{eff}$ and a genuine 1-loop correction which depend on the matrix $\Psi \nabla _{\mu }\Psi (z)$ at two different sites $z=z_{1},z_{2},$ where $\Psi $ is the interpolation of $\Phi $ with minimal action. Our result extends Polyakovs calculation which had furnished those contributions to the effective action which are of order ln $a^{'}/a$.

Massimo Campostrini,
`campo@mailbox.difi.unipi.it`