Theory and simulation of the dynamic heat capacity of the east Ising model.

A recently developed methodology for the calculation of the dynamic heat capacity from simulation is applied to the east Ising model. Results show stretched exponential relaxation with the stretching exponent, beta, decreasing with decreasing temperature. For low temperatures, the logarithm of the relaxation time is approximately proportional to the inverse of the temperature squared, which is the theoretical limiting behavior predicted by theories of facilitated dynamics. In addition, an analytical approach is employed where the overall relaxation is a composite of relaxation processes of subdomains, each with their own characteristic time. Using a Markov chain method, these times are computed both numerically and in closed form. The Markov chain results are seen to match the simulations at low temperatures and high frequencies. The dynamics of the east model are tracked very well by this analytic procedure, and it is possible to associate features of the spectrum of the dynamic heat capacity with specific domain relaxation events.