Theory of Critical Phenomena with Memory

Memory is a ubiquitous characteristic of complex systems, and critical phenomena are one the most intriguing in nature. Here, we propose an Ising model with memory, develop corresponding theory memory for discover series surprising novel results. We show that naive usual Hamiltonian direct inclusion power-law decaying long-range temporal interaction violates radically hyperscaling law all spatial dimensions even at below upper dimension. This entails both indispensable consideration dynamics, rather than practice just focusing on dynamic Lagrangian alone, transformations result correct which space time inextricably interwoven, leading to effective dimension repairs law. The gives rise set mean-field exponents, different from Landau ones, as well new universality classes. These exponents verified by numerical simulations two three dimensions.