含自旋-自旋相互作用噪声矩阵的小尺度二维伊辛模型研究
Investigation of Finite-size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions
摘要：
我们分析的自旋系统的热力学性质的变化时，它通过从经典的二维伊辛模型的自旋玻璃模型，自旋-自旋相互作用是随机的，在他们的值和符号。形式上，过渡减少到叠加在相互作用自旋的初始伊辛矩阵上的乘性噪声（均匀分布，平均值等于1）的幅度的逐渐变化。考虑到噪声，我们得到的解析表达式是有效的有限大小的晶格。我们比较我们的结果与计算机模拟的结果进行方形$N=L{\times}L$晶格与线性尺寸$L = 50÷1000$。我们发现实验的依赖性的临界值（临界温度，内能，熵和比热）以及依赖性的基态的能量和它的磁化强度上的噪声的幅度。当噪声方差达到1时，基态从完全关联态跃迁到非关联态，磁化强度从1跃迁到0。同时，在较低的噪声水平处存在的相变消失。
英文摘要：
We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the transition reduces to a gradual change in the amplitude of the multiplicative noise (distributed uniformly with a mean equal to one) superimposed over the initial Ising matrix of interacting spins. Considering the noise, we obtain analytical expressions that are valid for lattices of finite sizes. We compare our results with the results of computer simulations performed for square $N=L{\times}L$ lattices with linear dimensions $L = 50÷1000$. We find experimentally the dependencies of the critical values (the critical temperature, the internal energy, entropy and the specific heat) as well as the dependencies of the energy of the ground state and its magnetization on the amplitude of the noise. We show that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state and its magnetization jumps from 1 to 0. In the same time, a phase transition that is present at a lower level of the noise disappears.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
