Billoire Alain, Coluzzi Barbara
Service de Physique Théorique, CEA-Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 2):026131. doi: 10.1103/PhysRevE.68.026131. Epub 2003 Aug 29.
We study numerically the Sherrington-Kirkpatrick model as a function of the magnetic field h, with fixed temperature T=0.6T(c). We investigate the finite size scaling behavior of several quantities, such as the spin-glass susceptibility, searching for numerical evidences of the transition on the de Almeida-Thouless line. We find strong corrections to scaling which make difficult to locate the transition point. This shows, in a simple case, the extreme difficulties of spin-glass simulations in a nonzero magnetic field. Next, we study various sum rules (consequences of stochastic stability) involving overlaps between three and four replicas, which appear to be numerically well satisfied, and in a nontrivial way. Finally, we present data on P(q) for a large lattice size (N=3200) at low temperature T=0.4T(c), where the shape predicted by the replica symmetry breaking solution of the model for a nonzero magnetic field is visible.
我们对作为磁场(h)的函数的Sherrington-Kirkpatrick模型进行了数值研究，温度固定为(T = 0.6T(c))。我们研究了几个量的有限尺寸标度行为，比如自旋玻璃磁化率，寻找在de Almeida-Thouless线上转变的数值证据。我们发现对标度有很强的修正，这使得确定转变点变得困难。这在一个简单的例子中表明了在非零磁场下自旋玻璃模拟的极端困难。接下来，我们研究了各种求和规则（随机稳定性的结果），这些规则涉及三个和四个副本之间的重叠，它们在数值上似乎得到了很好的满足，而且方式非同寻常。最后，我们给出了在低温(T = 0.4T(c))下大晶格尺寸（(N = 3200)）时(P(q))的数据，其中对于非零磁场，模型的复制对称破缺解所预测的形状是可见的。
