"Perhaps the most important parts of the Ornstein theory are criteria for determining whether or not a shift or flow is Bernoulli (a Bernoulli shift, $B\_{ct}$ , or $B\_{t}^{\infty}$) because it allows us to prove that certain concrete systems are Bernoulli."[Quote from scholarpedia][1] [1]: <http://www.scholarpedia.org/article/Ornstein_theory>


Firstly, can you mention some profound applications and a bit of the intuition of the power of this theorem?


So say I have a dynamical system with action T isomorphic (by $\phi$) to a Bernouli system with action S, then $S(x)=\phi(T)(x)$. Any interesting examples with explicit $\phi$?


Can you mention some interesting applications of this theorem especially in the field of Probability intersecting with Statistical mechanics models like SLE and Spin glasses? 


Thanks



Importance of Ornstein's isomorphism theorem
You might want to start with this article by Ornstein:


An Application of Ergodic Theory to Probability Theory, Donald S. Ornstein, 
The Annals of Probability, Vol. 1, No. 1 (Feb., 1973), pp. 43-58


