Related papers: Mean-value identities as an opportunity for Monte …
We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…
The Ising model S=1/2 and the S=1 model are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
We estimate the parameter of a stationary time series process by minimizing the integrated weighted mean squared error between the empirical and simulated characteristic function, when the true characteristic functions cannot be explicitly…
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they offer an arbitrarily precise estimation of global and local tallies while making very few assumptions. However, since the inception of such…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
We report microcanonical Monte Carlo simulations of melting and superheating of a generic, Lennard-Jones system starting from the crystalline phase. The isochoric curve, the melting temperature $T_m$ and the critical superheating…
We have tested the theoretical values of critical exponents, predicted for the three--dimensional Heisenberg model, based on the published Monte Carlo (MC) simulation data for the susceptibility. Two different sets of the critical exponents…
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80,000 sites which are linked together according to the Voronoi/Delaunay prescription. In one set of…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional anti-ferromagnetic Ising model with a globally conserved magnetization $m_s$ (not the order parameter). From the power law behavior of the…
We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to $L=1600$. As…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…
A two-dimensional fluid of hard spheres each having a spin $\pm 1$ and interacting via short-range Ising-like interaction is studied near the second order phase transition from the paramagnetic gas to the ferromagnetic gas phase. Monte…
We present the numerical results for low temperature behavior of the transverse-field Ising model on a frustrated checkerboard lattice, with focus on the effect of both quantum and thermal fluctuations. Applying the recently-developed…