Related papers: Mapping distinct phase transitions to a neural net…

Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…

The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized…

Motivated by the idea that criticality and universality of phase transitions might play a crucial role in achieving and sustaining learning and intelligent behaviour in biological and artificial networks, we analyse a theoretical and a…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

We study the phase transition of the Ising model in networks with core-periphery structures. By Monte Carlo simulations, we show that prior to the order-disorder phase transition the system organizes into an inhomogeneous intermediate phase…

In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are…

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…

In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This…

By constructing an exactly solvable spin model, we investigate the critical behaviors of transverse field Ising chains interpolated with cluster interactions, which exhibit various types of topologically distinct Ising critical points.…

Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…

Originating from image recognition, methods of machine learning allow for effective feature extraction and dimensionality reduction in multidimensional datasets, thereby providing an extraordinary tool to deal with classical and quantum…

The detection of phase transitions is a central task in many-body physics. To automate this process, the task can be phrased as a classification problem. Classification problems can be approached in two fundamentally distinct ways: through…

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…

We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by…

We present a general framework for incorporating non-reciprocal interactions into the Ising model with Glauber dynamics, without requiring multiple species. We then focus on a model with vision-cone type interactions. We solve it in a fully…

In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…

Quantum convolutional neural networks (QCNNs) have been introduced as classifiers for gapped quantum phases of matter. Here, we propose a model-independent protocol for training QCNNs to discover order parameters that are unchanged under…

Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice…

We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks---a class of…