时间：11月6日（星期三） 16:30
地点：沙河校区理学楼302
主讲人：汤雷翰教授（西湖大学理学院及交叉科学中心）
内容摘要：
The concept of hidden Mattis phase in annealed spin-glass models was first proposed by Kasai and Okiji 40 years ago [1] but received little attention until recently [2, 3]. Although no thermodynamic transition is expected, the distribution of spin configurations acquires a Mattis-type order at low temperatures, as shown rigorously through a mapping between quenched and annealed models along the Nishimori line [4]. In this study, we investigate the dynamic consequences of the hidden Mattis order using detailed Monte Carlo simulations of the Sherrington-Kirkpatrick (SK) Ising spin-glass model with slowly updated annealed coupling constants. During the simulation, we monitor the eigenvalue spectrum of the instantaneous matrix of coupling constants, and our results generally support predictions based on random matrix theory. We observe a gap in the low-temperature Mattis phase that separates the largest eigenvalue from the rest of the spectrum. The principal eigenvector (i.e., the eigenvector of the largest eigenvalue) defines the instantaneous Mattis order, serving as a site-dependent, heterogeneous mean field for the spins. Hybridization of the first two eigenvectors signals a system-level restructuring of the hidden state, which can be detected from the 2-point and 4-point autocorrelation functions of the spins. Therefore, the hidden Mattis order can be associated with formation of a system-wide condensate of spins that undergoes large-scale, intermittent reorganization in configuration space. We present detailed finite-size scaling analysis to characterize the relevant time scales near and far below the transition temperature[5].
References
[1] Y. Kasai and A. Okiji, Prog. Theor. Phys. 69, 20 (1983).
[2] F. Krzakala and L. Zdeborová, J. Chem. Phys. 134, 034513 (2011).
[3] L. Foini and J. Kurchan, SciPost Phys. 12, 080 (2022).
[4] H. Nishimori, Statistical physics of spin glasses and information processing: an introduction, Oxford U Press, 2001.
[5] Ding Wang and Lei-Han Tang, SciPost Phys. 17, 106 (2024).
主讲人介绍：
汤雷翰，西湖大学讲席教授，美国物理学会会士。曾任香港研究资助局自然科学小组委员、香港物理学会理事会主席、亚太物理联合会理事、IUPAP C3统计物理委员会委员等。主要从事平衡和非平衡系统统计物理及定量生物学研究，包括复杂系统序的产生、演化、相变，高维非平衡系统动力学特性、集体行为、时空结构等。近期研究聚焦有状态变量和相互作用的共进化及隐藏序的产生，二维活性液体膜的自发旋转，多组分蛋白凝聚体间的浸润现象及调控等。
