Topic
Wolff algorithm
About: Wolff algorithm is a research topic. Over the lifetime, 66 publications have been published within this topic receiving 2874 citations.
Papers published on a yearly basis
Papers
TL;DR: A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality and its efficiency is demonstrated in the two-dimensional $\mathrm{O}(n)$ $\ensuremath{\sigma}$ models.
Abstract: A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality. We demonstrate its efficiency in the two-dimensional $\mathrm{O}(n)$ $\ensuremath{\sigma}$ models for $n=1$ (Ising) and $n=2$ ($x\ensuremath{-}y$) at their critical temperatures, and for $n=3$ (Heisenberg) with correlation lengths around 10 and 20. On lattices up to ${128}^{2}$ no sign of critical slowing down is visible with autocorrelation times of 1-2 steps per spin for estimators of long-range quantities.
2,771 citations
TL;DR: Three physical tests are proposed to measure correlations in random numbers used in Monte Carlo simulations to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations inrandom number sequences.
Abstract: We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of [ital n] successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
117 citations
TL;DR: In this paper, the scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is shown to be SLE with kappa=3, and the results are in support of their hypothesis.
Abstract: The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is SLE with kappa=3. We hypothesise that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries which are also SLE in the scaling limit, but with kappa=10/3. To test this, we generate samples using the Wolff algorithm and test them against predictions of SLE: we examine the statistics of the Loewner driving function, estimate the fractal dimension and test against Schramm's formula. The results are in support of our hypothesis.
63 citations
TL;DR: The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is Schramm-Loewner evolution (SLE) with κ = 3 as mentioned in this paper.
Abstract: The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is Schramm–Loewner evolution (SLE) with κ = 3. We hypothesize that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries which are also SLE in the scaling limit, but with κ = 10/3. To test this, we generate samples using the Wolff algorithm and test them against predictions of SLE: we examine the statistics of the Loewner driving function, estimate the fractal dimension and test against Schramm's formula. The results are in support of our hypothesis.
63 citations
TL;DR: Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, this work studies the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases.
53 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 3 |
| 2019 | 1 |
| 2018 | 5 |
| 2017 | 1 |
| 2016 | 1 |