We analyze a simple model appropriate for the description of the critical dynamics of isotropic antiferromagnets in the ordered phase. We use renormalization-group methods and mode-coupling ideas to analyze the various correlation functions of interest below the Neel temperature. The transverse correlation functions are dominated by spin waves in agreement with the predictions of hydrodynamics in the appropriate qg&1 limit . We find that the positions of the spin-wave peaks for the transverse magnetization and staggered magnetization correlation function diAer significantly as q$ increases. The spin-wave peaks persist as qt' is increased in the transverse staggered magnetization, but become quickly overdamped as qt' increases for the transverse magnetization correlation function. These results are consistent with our previous calculations at T = T~where we found damped spin waves in the staggered magnetization correlation function, but not in the magnetization correlation function. Our most interesting result is that as a result of strong coupling of transverse spin waves into the longitudinal modes, hydrodynamics breaks down in treating the longitudinal magnetization correlation functions. This breakdown, first discovered by Villain using a mode-coupling approach, is manifested in the wave-number-dependent spin-diffusion coefIIicient going as q " in three dimension for small q. The treatment of the longitudinal order-parameter correlation function is diRicult within an e expansion. We discuss these difficulties.
liquid T~2 behavior. This deviation is several times larger than the expected fluctuation effect, and does not appear to be related to the superfluid transition. As a result, one cannot make a reliable background subtraction to isolate the effects of superfluid fluctuations. 8 We thank Doug Paulson and John Wheatley for informing us of their preliminary results, and for permission to quote their results prior to publication. We are grateful to V. J. Emery for helpful discussions, and for pointing out an error in a preliminary version of this Letter.We present a general approach for applying real-space renormalization-group methods to dynamic critical phenomena. In particular, we discuss the two-dimensional kinetic Ising model treating the interaction between blocks of spins as a small parameter.
A real-space dynamic renormalization-group scheme is used to evaluate static and dynamic correlation functions for a kinetic Ising model on a two-dimensional square lattice. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations and are in excellent agreement with known values.PACS numbers: 64.60.-i The calculation of static and dynamic correlation functions in systems that undergo a phase transition is a problem of great interest. These functions can be measured in scattering experiments and exhibit a wide variety of phenomena in the region near the phase transition. Recently, 1 ' 2 a real-space dynamic renormalization-group (RSDRG) method was introduced for the investigation of lattice dynamical models. In this Letter we apply this method to the kinetic Ising (Kl) model on a square lattice and show how, within the formalism, one can calculate space-and timedependent correlation fucntions.The KI model 3 describes the stochastic time evolution of a set of Ising spins {cr}. The equilibrium properties are governed by the nearestneighbor Ising-model Hamiltonian, H a , characterized by a coupling K. The time evolution of this model is assumed to be generated by a single-spin-flip operator (SFO):o> ln W i [v]a i +J 2 cr
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