Sire Clément
Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France.
Phys Rev Lett. 2004 Sep 24;93(13):130602. doi: 10.1103/PhysRevLett.93.130602. Epub 2004 Sep 20.
We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')<<L(t)<<L(t')(phi) well inside the scaling regime, the spin autocorrelation function behaves like s(t)s(t') approximately L(t')(-(d-2+eta))L(t')/L(t). For the O(n) model in the n-->infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.
我们研究了在临界温度下猝灭后守恒自旋系统的自相关函数。定义关联长度(L(t))近似为(t^{(1/z)})，我们发现，对于处于标度区域内且满足(L(t') << L(t) << L(t')^{\phi})的时间(t')和(t)，自旋自相关函数的行为类似于(s(t)s(t') \approx L(t')^{-(d - 2 + \eta)}[L(t')/L(t)]^{\lambda'_c})。对于(n \to \infty)极限下的(O(n))模型，我们表明(\lambda'_c = d + 2)且(\phi = z/2)。我们给出了一个启发式论证，表明该结果实际上对任何维度(d)和自旋矢量维度(n)都是有效的。我们给出了(d = 1)和(d = 2)时守恒伊辛模型的数值模拟结果，这些结果与当前理论完全一致。
