The European Physical Journal E ( IF 1.8 ) Pub Date : 2022-08-23 , DOI: 10.1140/epje/s10189-022-00221-2 Juš Polanšek 1 , Arbresha Holbl 1 , Szymon Starzonek 2 , Aleksandra Drozd-Rzoska 2 , Sylwester J Rzoska 2 , Samo Kralj 1, 3
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Abstract
We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems’ stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.
Graphical abstract
中文翻译：
历史相关相变特征
摘要
我们以取向顺序考虑域类型配置中的历史相关行为，这些行为是在通过连续对称破坏相变达到的配置中形成的。在平衡状态下，这些系统在没有杂质的情况下表现出空间均匀的顺序。我们专注于通过 (i) 在足够快的淬火中通过 Kibble-Zurek 机制或通过 (ii) 在强过冷相中通过 Kibble 机制形成域的情况。在这两种情况下，由于在畴壁上形成的钉扎拓扑缺陷，畴可能会被阻止。在呈现极性或四极性顺序的系统中，点和线缺陷（向错）分别占主导地位。特别是，向错可以形成复杂的纠缠结构，并且在稳定畴方面更有效。正如 Imry-Ma 定理所暗示的，由快速淬火形成的域模式可以被施加足够强的随机场类型无序的杂质所阻止。另一方面，如果由于足够大的系统刚度而建立了足够大的能量障碍阻止域，则也可以形成在过冷系统中形成的域。在已建立的域类型模式中产生的有效交互可以用随机矩阵来描述。得到的特征向量揭示了在这种结构中形成的预期结构激发。最重要的作用通常由随机矩阵最大特征向量来发挥。如果此特征向量表现出局部或扩展特征，则预期会有定性不同的行为。在前一种情况下，人们期望逐渐的、非临界型转变为玻璃型结构。然而，
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