Kryzhanovsky Boris, Malsagov Magomed, Karandashev Iakov
Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218 Moscow, Russia.
Entropy (Basel). 2018 Aug 7;20(8):585. doi: 10.3390/e20080585.
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 = × lattices with linear dimensions = 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.
我们分析了一个自旋系统从经典二维伊辛模型转变为自旋玻璃模型时其热力学性质的变化，在自旋玻璃模型中，自旋 - 自旋相互作用在其值和符号上都是随机的。形式上，这种转变归结为叠加在初始相互作用自旋的伊辛矩阵上的乘性噪声（均值等于 1 的均匀分布）幅度的逐渐变化。考虑到噪声，我们得到了对有限尺寸晶格有效的解析表达式。我们将我们的结果与针对线性尺寸(L = 50 \div 1000)的正方形(L×L)晶格进行的计算机模拟结果进行比较。我们通过实验发现了临界值（临界温度、内能、熵和比热）的依赖性，以及基态能量及其磁化强度对噪声幅度的依赖性。我们表明，当噪声的方差达到 1 时，基态从完全相关状态跃变为不相关状态并且其磁化强度从 1 跃变为 0。同时，在较低噪声水平下存在的相变消失。
