Studies of the local order parameter of Ni3+ impurities in the tetragonal phase of Rb1−Cs CaF3 mixed crystals

A study of dynamic finite size scaling behavior of the scaling functions—calculation of dynamic critical index of Wolff algorithm

“…Finite size scaling and universality arguments have been used to study the critical parameters of spin systems over two decades [1]. Jansen, Schaub and Schmittmann [2] showed that for a dynamic relaxation process, in which a system is evolving according to a dynamics of Model A [3] and is quenched from a very high temperature to the critical temperature, a universal dynamic scaling behavior within the short-time regime exists [4,5,6]. The existence of finite size scaling even in the early stages of the Monte Carlo simulation has been tested for various spin systems [5,6,7,8,9,10,11,12], the dynamic critical behavior is well-studied and it has been shown that the dynamic finite size scaling relation holds for the magnetization and for the moments of the magnetization.…”

“…Jansen, Schaub and Schmittmann [2] showed that for a dynamic relaxation process, in which a system is evolving according to a dynamics of Model A [3] and is quenched from a very high temperature to the critical temperature, a universal dynamic scaling behavior within the short-time regime exists [4,5,6]. The existence of finite size scaling even in the early stages of the Monte Carlo simulation has been tested for various spin systems [5,6,7,8,9,10,11,12], the dynamic critical behavior is well-studied and it has been shown that the dynamic finite size scaling relation holds for the magnetization and for the moments of the magnetization. For the k th moment of the magnetization of a spin system, dynamic finite size scaling relation can be written as [2] M (k) (t, ǫ, m 0 , L) = L (−kβ/ν) M (k) (t/τ, ǫL 1/ν , m 0 L x 0 ) (1) where L is the spatial size of the system, β and ν are the well-known critical exponents, t is the simulation time, ǫ = (T − T c )/T c is the reduced temperature and x 0 is an independent exponent which is the anomalous dimension of the initial magnetization (m 0 ).…”