Theory of Critical Phenomena with Memory
Shaolong Zeng, Sue Ping Szeto, and Fan Zhong*
State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
Abstract ：Memory is a ubiquitous characteristic of complex systems, and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory, develop a corresponding theory of critical phenomena with memory for complex systems, and discover a series of surprising novel results. We show that a naive theory of a usual Hamiltonian with a direct inclusion of a power-law decaying long-range temporal interaction violates radically a hyperscaling law for all spatial dimensions even at and below the upper critical dimension. This entails both indispensable consideration of the Hamiltonian for dynamics, rather than the usual practice of just focusing on the corresponding dynamic Lagrangian alone, and transformations that result in a correct theory in which space and time are inextricably interwoven, leading to an effective spatial dimension that repairs the hyperscaling law. The theory gives rise to a set of novel mean-field critical exponents, which are different from the usual Landau ones, as well as new universality classes. These exponents are verified by numerical simulations of the Ising model with memory in two and three spatial dimensions.
收稿日期: 2022-10-21
Express Letter
出版日期: 2022-11-20
:
05.50.+q
(Lattice theory and statistics)
64.60.Ht
(Dynamic critical phenomena)
64.60.ae
(Renormalization-group theory)
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