Related papers: Unsupervised machine learning approaches to the $q…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning. Taking as a prototype the Ising model and using the Support Vector Machine as…
In previous work, it has been shown that the recently proposed LLR method is very efficient at overcoming strong metastabilities that arise near first-order phase transition points. Here we present a systematic study of the performance of…
We propose an unsupervised learning methodology with descriptors based on Topological Data Analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a…
We employ unsupervised learning tools to identify different phases and their transition in quantum systems subject to the combined action of unitary evolution and stochastic measurements. Specifically, we consider principal component…
Machine learning (ML) methods provide advanced means for understanding inherent patterns within large and complex datasets. Here, we employ the principal component analysis (PCA) and the diffusion map (DM) techniques to evaluate the glass…
The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are…
Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum…
In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original…
A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order…
We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The…
The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…
The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of…
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…
Inverse UQ is the process to inversely quantify the model input uncertainties based on experimental data. This work focuses on developing an inverse UQ process for time-dependent responses, using dimensionality reduction by functional…
Entropy and order parameter are two key concepts in phase transition theory. This paper proposes an unified method to both find order parameter and estimate entropy automatically with unsupervised learning. The contributions of this paper…
We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For…
We investigate the nature of the phase transition of the ferromagnetic Potts model with invisible states. The ferromagnetic Potts model with invisible states can be regarded as straightforward extension of the standard ferromagnetic Potts…
We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians…
We derive a universal relation for the critical temperatures of the $q$-state Potts model based on the counting of domain-wall microstates. By balancing interface energy against configurational entropy, we show that the critical temperature…