Singh R R P, Young A P
University of California Davis, Davis, California 95616, USA.
University of California Santa Cruz, Santa Cruz, California 95064, USA.
Phys Rev E. 2017 Jul;96(1-1):012127. doi: 10.1103/PhysRevE.96.012127. Epub 2017 Jul 13.
We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d-dimensional hypercubic lattices for d=5-8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w=tanh^{2}J/T for arbitrary values of u=tanh^{2}h/T complete to order w^{10}. We find that the scaling dimension Δ associated with the ordering-field h^{2} equals 2 in the SK model and for d≥6. However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)PRLTAO0031-900710.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h-T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978)JPHAC50305-447010.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d→6. Within the convergence of our series analysis, we present evidence supporting an AT line in d≥6. In d=5, the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d=5.
我们使用高温级数展开来研究d维超立方晶格（d = 5 - 8）以及无限范围的谢林顿 - 柯克帕特里克（SK）模型中磁场下的±J伊辛自旋玻璃。对于任意u = tanh²h/T值，在变量w = tanh²J/T中得到了完整到w¹⁰阶的展开式。我们发现，在SK模型以及d≥6时，与有序场h²相关的标度维数Δ等于2。然而，与费舍尔和索波林斯基的工作一致[《物理评论快报》54, 1063 (1985)PRLTAO0031 - 900710.1103/PhysRevLett.54.1063]，在有限场中存在标度破坏，导致高维中德阿尔梅达 - 图勒斯（AT）线[《物理学报A》11, 983 (1978)JPHAC50305 - 447010.1088/0305 - 4470/11/5/028]的h - T依赖性反常，而当d→6时标度恢复正常维度。在我们级数分析的收敛范围内，我们给出了支持d≥6时AT线的证据。在d = 5时，指数γ和Δ大幅大于平均场值，但我们在d = 5中未看到AT线的明确证据。
