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We propose the construction of thermodynamic ensembles that minimize the R\'enyi free energy, as an alternative to Gibbs states. For large systems, the local properties of these R\'enyi ensembles coincide with those of thermal equilibrium,…
The R\'{e}nyi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the R\'{e}nyi distribution and postulate them to be…
The $n$-index R\'enyi mutual information and transfer entropy for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of thermodynamic quantities. By means of Monte…
We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above…
Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate…
By developing a method to represent the Renyi entropies via a replica-trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations…
In order to gain a deeper understanding of complex systems and infer key information using minimal data, I classify all configurations based on classical probability, starting from the dimensions of energy and different categories of…
Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo…
Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…
We study the R\'enyi entropies in the spin-$1/2$ anisotropic Heisenberg chain after a quantum quench starting from the N\'eel state. The quench action method allows us to obtain the stationary R\'enyi entropies for arbitrary values of the…
We develop a Monte Carlo framework to analyze the statistics of quantum work in correlated electron systems. Using the Ising-Kondo model in heavy fermions as a paradigmatic platform, we thoroughly illustrate the process of determining the…
Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…
Renyi Mutual information (RMI), computed from second Renyi entropies, can identify classical phase transitions from their finite-size scaling at the critical points. We apply this technique to examine the presence or absence of finite…
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of…
Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic…
We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for…
The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the R\'enyi entropy is a precious tool…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the…
We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier…