Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a finite distance $L$. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behaviour characterized by a non universal exponent which depends on the ratio of the system size to a dynamic length scale.