Short-time critical dynamics of the three-dimensional Ising model

Abstract

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent θ of the critical initial increase and the dynamic exponent z, the static critical exponents ν and β as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations. PACS: 64.60.Cn, 75.10.Hk, 64.60.Ht, 75.40.Mg * Work supported in part by the Deutsche Forschungsgemeinschaft; DFG Schu 95/9-1 and SFB 418 1 For a recent review see Ref. [2].

Dynamic critical behavior in Ising spin glasses

“…We have thus been able to minimize one of the major sources of systematic errors in numerical simulations, namely corrections to finite size scaling. This is very similar to what is observed when studying critical ferromagnets, as for example the threedimensional Ising model 44 , where no notable finite-size corrections to scaling are encountered in non-equilibrium simulations, in contrast to equilibrium simulations where these corrections to scaling can be very strong.…”

Monte Carlo simulations of short-time critical dynamics with a conserved quantity

“…Therefore, it is interesting to study the dynamics, with a locally conserved order parameter or non-order parameter: in a flip, we exchange two spins in a local regime, the size of which must be much smaller than the lattice size. [46]. Under the item 'Ising' are the values for the standard Ising model in equilibrium [45].…”

“…[13] and θ = 0.108 (2) in Ref. [46] for the Ising model without a conserved quantity. Rigorously speaking, the exponent θ is defined in the limit of m 0 = 0.…”

“…Then from y and c d we calculate the exponents 2β/ν and ν. For comparison, available results for dynamics without a conserved quantity [46], i.e., the so-called model A dynamics, are also given, where the critical point K c and the exponent ν are measured from another dynamic process starting from a completely ordered state. Within statistical errors, all the exponents for dynamics with and without a conserved quantity agree well each other.…”

Short-time dynamics study of Heisenberg noncollinear magnets

“…In particular we are interested in the critical relaxation process. This interest is due to the presence of a general scaling form that enables us to calculate T c and the critical exponents of different systems far from equilibrium [10,11]. This process will be discussed further in the following chapters.…”