Heuristic Approach to the Critical Dynamics of the Ising Model

The classical Ising model (IM) and the quantum transverse Ising model (TIM) are generically used to study cooperative phenomena. The three-dimensional (d = 3) TIM has several applications to real systems[1], including the description of structural order-disorder phase transitions observed in ferroelectrics at a critical temperature Tc. In the d = 1 case, the TIM with nearest-neighbor interactions exhibits T = 0 longrange-order for small enough transverse elds < c. In the current work we propose a new approach to the problem of the critical dynamics. It is based on a heuristic method introduced by Thompson [2] and developed by one of the authors[3]. Thompson's method is based on the idea that the action, as well as a relevant free energy of the system of many scales of length, are limited functions. This heuristic method was formulated through a set of assumptions (see prescriptions A,B,C in Ref.[2]) that avoid dealing with the renormalization-group (RG) equations of motion.