phase transition - What is the definition of correlation length for the Ising model?

The correlation length $\xi$ is related to critical temperature $T_c$ as

$$\xi\sim|T-T_{c}|{}^{-\nu},$$

where $\nu$ is the critical exponent.

1. Is this the formal definition of correlation length? If not, what is the formal definition of correlation length (for phase transition in the Ising model)?


2. Can you give a physical understanding of correlation length?