Critical behavior of the three-dimensional random-anisotropy Heisenberg model,Physical Review E

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Critical behavior of the three-dimensional random-anisotropy Heisenberg model
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-15 , DOI: 10.1103/physreve.106.034123
J J Ruiz-Lorenzo ₁ , M Dudka ₂ , Yu Holovatch ₃

Affiliation

We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different anisotropy strengths for each disorder class. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a zero magnetization low-temperature phase. Studying this region using a spin-glass order parameter we have found evidence for a spin-glass phase transition. We have estimated effective critical exponents for the spin-glass phase transition for the different values of the strength of the isotropic disorder, discussing the crossover regime.

中文翻译：

三维随机各向异性 Heisenberg 模型的临界行为

我们通过使用平行回火方法的数值模拟研究了三维随机各向异性海森堡模型的临界性质。我们使用两种不同的无序分布（立方分布和各向同性分布）模拟了模型，每个无序类别具有两种不同的各向异性强度。对于各向异性无序的情况，我们通过找到与无序强度无关的临界指数和普遍的无量纲比率来发现普遍性的证据。在各向同性无序分布的情况下，情况非常复杂：我们在磁化通道中发现了两个相变，它们合并为较大的晶格，保持零磁化低温相。使用自旋玻璃顺序参数研究该区域，我们发现了自旋玻璃相变的证据。我们已经估计了对于各向同性无序强度的不同值的自旋玻璃相变的有效临界指数，讨论了交叉机制。

更新日期：2022-09-15

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