Related papers: Theory of Critical Phenomena with Memory
We study how the formalism of the Hierarchical Reference Theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid state theory which implements the basic ideas of Wilson momentum shell renormalization group (RG) to microscopic…
We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
Humans and other organisms make decisions choosing between different options, with the aim to maximize the reward and minimize the cost. The main theoretical framework for modeling the decision-making process has been based on the highly…
Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
We discuss memory models which are based on tensor decompositions using latent representations of entities and events. We show how episodic memory and semantic memory can be realized and discuss how new memory traces can be generated from…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…
We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
The computational complexity of the self-attention mechanism in Transformer models significantly limits their ability to generalize over long temporal durations. Memory-augmentation, or the explicit storing of past information in external…
Barkhausen noise as found in magnets is studied both with and without the presence of long-range (LR) demagnetizing fields using the non-equilibrium, zero-temperature random-field Ising model. Two distinct subloop behaviors arise and are…
We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point.…
A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…
When interacting spin systems possess non-zero magnetization or topological entanglement entropy below the transition temperature, they often serve as classical or quantum self-correcting memory. In particular, their memory time grows…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…
We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…