Mukherjee Sudip, Rajak Atanu, Chakrabarti Bikas K
Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042107. doi: 10.1103/PhysRevE.92.042107. Epub 2015 Oct 5.
We study the critical behavior of the Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their "classical" to "quantum" values at a finite temperature (unlike the cases of pure systems, where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.
我们使用蒙特卡罗模拟和精确对角化（在零温度下）研究横向场（在有限温度下）中谢林顿 - 柯克帕特里克模型的临界行为。我们通过估计宾德累积量来确定模型的相图。我们还从标度数据的塌缩中确定关联长度指数。我们在此的数值研究表明，临界宾德累积量（指示转变行为的普适类）和关联长度指数在有限温度下从它们的“经典”值转变为“量子”值（与纯系统的情况不同，在纯系统中这种转变发生在零温度下）。我们提出了一个定性的论证来支持这样的观察结果，采用了一个简单的隧穿图像。
