论文标题
研究有限大小的2D ISING模型，具有自旋旋转相互作用的嘈杂基质
Investigation of Finite-size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions
论文作者
论文摘要
当自旋系统从经典的二维ISING模型传递到自旋玻璃模型时，我们分析了自旋系统的热力学特性的变化，在这些模型中，自旋旋转相互作用在其值和符号中是随机的。正式地，过渡减少到在相互作用自旋的初始ISing矩阵上叠加的乘噪声幅度的逐渐变化（均匀分布的平均值分布）。考虑到噪声，我们获得了有限尺寸晶格有效的分析表达式。我们将结果与对平方$ n = l {\ times} l $ lattices进行线性尺寸$ l = 50÷1000 $的计算机模拟结果进行比较。我们通过实验发现临界值（临界温度，内部能量，熵和特定热量）的依赖性以及基态能量的依赖性及其对噪声振幅的磁化。我们表明，当噪声的方差达到一个时，从完全相关状态到不相关状态的基态有一个跳跃，并且其磁化力从1跳到0。与此同时，噪声较低级别存在的相变消失了。
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.
