Related papers: Tuning the generalized Hybrid Monte Carlo algorith…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
We pose two questions about the dynamical critical behavior of multigrid Monte Carlo: Will a multigrid Monte Carlo simulation of the two dimensional Sine Gordon model exhibit critical slowing down, as expected by a theoretical analysis of…
We propose a new algorithm which works effectively in global updates in Monte Carlo study. We apply it to the quantum spin chain with next-nearest-neighbor interactions. We observe that Monte Carlo results are in excellent agreement with…
The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters, based on…
We investigate local update algorithms for the fully frustrated XY model on a square lattice. In addition to the standard updating procedures like the Metropolis or heat bath algorithm we include overrelaxation sweeps, implemented through…
Three possibilities to speed up the Hybrid Monte Carlo algorithm are investigated. Changing the step-size adaptively brings no practical gain. On the other hand, substantial improvements result from using an approximate Hamiltonian or a…
Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive…
We investigate aspects of universality of Glauber critical dynamics in two dimensions. We compute the critical exponent $z$ and numerically corroborate its universality for three different models in the static Ising universality class and…
We consider a generalization of the standard Metropolis algorithm acceptance/rejection decision rule and numerically explore its properties using auxiliary field quantum Monte Carlo. The generalization involves a free parameter which, given…
When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is suboptimal the performance leaves much to be desired. In this…
Auxiliary field quantum Monte Carlo methods for Hubbard models are generally based on a Hubbard-Stratonovitch transformation where the field couples to the z-component of the spin. This transformation breaks SU(2) spin invariance. The…
The dynamical critical exponent $z$ is a fundamental quantity in characterizing quantum criticality, and it is well known that the presence of dissipation in a quantum model has significant impact on the value of $z$. Studying quantum Ising…
We present algorithmic improvements to the overlap Hybrid Monte Carlo algorithm, including preconditioning techniques and improvements to the correction step, used when one of the eigenvalues of the Kernel operator changes sign, which is…
We report tests of the recently proposed multicanonical multigrid Monte Carlo method for the two-dimensional $\Phi^4$ field theory. Defining an effective autocorrelation time we obtain real time improvement factors of about one order of…
Simulations of strongly interacting lattice field theories are typically performed using Markov chain Monte Carlo algorithms. Therefore estimators of statistical errors must incorporate the effect of autocorrelations by integrating the…
We investigate reversibility violations in the Hybrid Monte Carlo algorithm. Those violations are inevitable when computers with finite numerical precision are being used. In SU(2) gauge theory, we study the dependence of observables on the…
The dynamic relaxation process for the two dimensional Potts model at criticality starting from an initial state with very high temperature and arbitrary magnetization is investigated with Monte Carlo methods. The results show that there…
We report performance benchmarks for several algorithms that we have used to simulate the Schr"odinger functional with two flavors of dynamical quarks. They include hybrid and polynomial hybrid Monte Carlo with preconditioning. An appendix…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…