Critical dynamics of nonperiodic Ising chains

The critical dynamics of the nonperiodic ferromagnetic Ising chains with two different coupling constants (J(1)>J(2)>0) arranged in nonperiodic sequences are studied by trace map method. For Glauber dynamics, it is found that the dynamical critical exponent z = 1 + J(1)/J(2) for the Fibonacci, general Fibonacci (e.g., silver-mean, copper-mean), and period-doubling ferromagnetic Ising chains. The applicability of the trace map method and the origin of the nonuniversality are briefly discussed.