Microcanonical Prescription

We can now take one of two approaches (1) construct a probabilistic CA along lines with the Metropolis Monte Carlo algorithm outlined above (see section 7.1.3.1), or (2) define a deterministic but reversible rule consistent with the microcanonical prescription. As we shall immediately see, however, neither approach yields the expected results. 

Boltzman s constant and T is the temperature. Using equations 7.101 and 7.102, we see that this is equivalent to the following PCA rule  

3 or 4 flip the spin with probability p if Aj = 1 and flip the spin with probability p if Ai = 0. 

What about a microcanonical ensemble based approach The simplest prescription would be to define a rule that flips the spins only at a constant energy that is, for 6H = 0 or Ai = 2. The reader may recall that we have already studied some of the behaviors of this rule in section 3.4 it is, in fact, equal to the Pbedkin-reversible rulq Q2R ([vich84], [vich86aj). Prom the comments made in our earlier discussion, it 

This configuration has a total energy W(to) = 8. Since each ct = 1 site has two (7 = 1 neighbors and two (7 = 0 neighbors, it gets flipped on the next time step. But each (7=0 site has, at most, one (7 = 1 neighbor and will be left unchanged. On the next iteration step, therefore, all of the sites in the cluster will have (7 = 0 and W(to + 1) = 0. 

---