Felix Bernstein Inst. Math. Stat. Biosci., Göttingen, Germany.
Univ. Göttingen, Inst. Math. Stochast., D-37073 Göttingen, Germany.
Phys Rev E. 2016 Mar;93(3):032123. doi: 10.1103/PhysRevE.93.032123. Epub 2016 Mar 14.
We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.
我们通过蒙特卡罗方法和解析近似研究了零场中伊辛自旋玻璃的近自旋玻璃转变的有限尺寸效应，以及场中的德阿尔梅达-图利转变。在零场中，与薛定谔-柯尔克帕特里克平均场自旋玻璃模型的自旋玻璃磁化率相关的有限尺寸标度函数的形式与具有幂律长程相互作用的一维自旋玻璃模型相同，在高于上临界维度的爱德华兹-安德森短程自旋玻璃模型中，它们可以作为替代模型。我们还计算了自旋玻璃磁化率交叉函数的简单解析近似。我们还研究了自旋玻璃磁化率在德阿尔梅达-图利转变线附近的行为，但在这里，我们只能在转变线以上和以下的渐近极限中获得其解析行为。我们还在非平均场情况下模拟了一维系统中的场，以说明当伊姆里-马液滴长度尺度超过系统尺寸时，即使不存在德阿尔梅达-图利转变，也可能错误地得出存在德阿尔梅达-图利转变的结论。
