時間：11月6日（星期三） 16:30
地點：沙河校區(qū)理學(xué)樓302
主講人：湯雷翰教授（西湖大學(xué)理學(xué)院及交叉科學(xué)中心）
內(nèi)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).
主講人介紹：
湯雷翰，西湖大學(xué)講席教授，美國物理學(xué)會會士。曾任香港研究資助局自然科學(xué)小組委員、香港物理學(xué)會理事會主席、亞太物理聯(lián)合會理事、IUPAP C3統(tǒng)計物理委員會委員等。主要從事平衡和非平衡系統(tǒng)統(tǒng)計物理及定量生物學(xué)研究，包括復(fù)雜系統(tǒng)序的產(chǎn)生、演化、相變，高維非平衡系統(tǒng)動力學(xué)特性、集體行為、時空結(jié)構(gòu)等。近期研究聚焦有狀態(tài)變量和相互作用的共進化及隱藏序的產(chǎn)生，二維活性液體膜的自發(fā)旋轉(zhuǎn)，多組分蛋白凝聚體間的浸潤現(xiàn)象及調(diào)控等。
