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Scaling of spatiotemporal correlation in ordering dynamics

1990; American Physical Society; Volume: 42; Issue: 10 Linguagem: Inglês

10.1103/physrevb.42.6438

1095-3795

Hiroshi Furukawa,

Material Dynamics and Properties

The two-time scaling assumption in the system undergoing phase separation is studied numerically. This assumption is written for the order-parameter correlation function as ${\mathit{S}}_{\mathit{k}}$(t,t')[${\mathit{S}}_{\mathit{k}}$(t)${\mathit{S}}_{\mathit{k}}$(t')${]}^{\mathrm{\ensuremath{-}}1/2}$ =${\mathit{V}}_{\mathrm{\ensuremath{\psi}}\mathrm{\ensuremath{\psi}}}$(kR(t),t'/t), where k is the wave number, t and t' are times after the quench, R(t) is the length scale, and ${\mathit{S}}_{\mathit{k}}$(t) is the same-time correlation function, which scales as ${\mathit{S}}_{\mathit{k}}$(t)=R(t${)}^{\mathit{d}}$S\ifmmode \tilde{}\else \~{}\fi{}(kR(t)), with d being the spatial dimension. We also examine a power-law expansion of ${\mathit{V}}_{\mathrm{\ensuremath{\psi}}\mathrm{\ensuremath{\psi}}}$(0,x)\ensuremath{\propto}(1+\ensuremath{\alpha}/2)${\mathit{x}}^{\mathrm{\ensuremath{\Delta}}}$-\ensuremath{\Delta}${\mathit{x}}^{1+\mathrm{\ensuremath{\alpha}}/2}$ (x\ensuremath{\le}1). Here 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1+\ensuremath{\alpha}/2, and \ensuremath{\alpha}=d/z-2 for the nonconserved order parameter and \ensuremath{\alpha}=(d+4)/z-2 for the conserved order parameter, where z is the growth-law exponent: R(t${)}^{\mathit{z}}$\ensuremath{\propto}t. For the two-dimensional Ising spin system with Glauber dynamics, we have \ensuremath{\alpha}=-1, and by simulation we found \ensuremath{\Delta}\ensuremath{\simeq}0.15. We have also done the same analysis for a two-dimensional system with conserved order parameter.