Strong coupling from non-equilibrium Monte Carlo simulations

We compute the running coupling of non-Abelian gauge theories in the Schr\"odinger-functional scheme, by means of non-equilibrium Monte Carlo simulations on the lattice.Comment: v1: 29 pages, 7 figures; v2: 1+46 pages, 9 figures: added a detailed discussion of the algorithm, computational efficiency analysis, comparison with perturbation theory at loops, new references, corrected typos (version published in the journal

Free energy of the self-interacting relativistic lattice Bose gas at finite density

The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase quenched counterpart. Using a set of lattices ranging from 44 to 164, we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of Oð10−480Þ. When phase factor measurements are extended to the dense phase, a change of behavior of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the nonanalyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed

Computing general observables in lattice models with complex actions

The study of QFTs at finite density is hindered by the presence of the so-called sign problem. The action definition of such systems is, in fact, complex-valued making standard importance sampling Monte Carlo methods ineffective. In this work, we shall review the generalized density of states method for complex action systems and the Linear Logarithmic Relaxation algorithm (LLR). We will focus on the recent developments regarding the bias control of the LLR method and the evaluation of general observables in the DoS+LLR framework. Recent results on the well-known relativistic Bose gas will be presented, proving that in our approach the phase factor can be consistently evaluated over hundreds of orders of magnitude. A first exploratory study on the Thirring model in the DoS formalism will be presented as well. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).Peer reviewe

Obtenir des signaux petits à partir des données oscillantes : le problème de signe dans les systèmes de particules

Monte Carlo simulations are the numerical method of choice for the study of lattice field theories in a non-perturbative framework. Over the years, Monte Carlo methods in Lattice Field Theories have reached a level of maturity such that in several QCD applications they provide the most reliable predictions for the low-energy behaviour of the theory. However, for many interesting theories, a complex-valued action prevents the use of standard sampling techniques. This is generally known as the sign problem and is present if the Boltzmann weight associated with the field configurations is either non-positive or non-real. A class of models exhibiting this property are finite density theories. These are going to be our primary interest.In this work, we shall focus on the density of states approach to the sign problem. This is a numerical technique that enables us to use standard Monte Carlo techniques to evaluate the density of states relating to the imaginary part of the action. By doing this, the sign problem is reduced to a simpler one-dimensional oscillatory integral, amenable to standard deterministic quadrature methods.At the core of our implementation of the density of states method is the LLR algorithm. We will present the general implementation and recent developments regarding on the control of possible sources of bias. Then we will extend the current formulation to allow for the evaluation of generic observables. Both these topics will be supported by results from numerical studies of the relativistic Bose gas at finite density.Lastly, we will discuss the problem of applying this approach to fermionic models where the sign problem is generated by the complex-valued fermionic determinant. As a specific application, we will study the Thirring model in two different representations discussing the related challenges.Les simulations de Monte Carlo sont la méthode numérique de choix pour l'étude des théories des champs sur réseau dans un système non perturbatif. Au fil des ans, les méthodes de Monte Carlo dans les théories de champ sur réseau ont atteint un niveau de maturité tel que dans plusieurs applications QCD, elles fournissent les prédictions les plus fiables pour le comportement à basse énergie de la théorie. Cependant, pour de nombreuses théories intéressantes, une action à valeurs complexes empêche l'utilisation de techniques d'échantillonnage standard. Ceci est généralement connu sous le nom de problème de signe et est présent si le poids de Boltzmann associé aux configurations de champ est non positif ou non réel. Une classe de modèles présentant cette propriété sont les théories de densité finie. Celles-ci seront notre principal intérêt.Dans ce travail, nous nous concentrerons sur l'approche de la densité d'états au problème de signe. Il s'agit d'une technique numérique qui permet d'utiliser les techniques standards de Monte Carlo pour évaluer la densité d'états relatifs à la partie imaginaire de l'action. En faisant cela, le problème du signe est réduit à une intégrale oscillatoire unidimensionnelle plus simple, qui se prête aux méthodes de quadrature déterministes standard.Au cœur de notre implémentation de la méthode de la densité des états se trouve l'algorithme LLR. Nous présenterons la mise en œuvre générale et les développements récents concernant le contrôle des sources possibles de biais. Ensuite, nous étendrons la formulation actuelle pour permettre l'évaluation d'observables génériques. Ces deux sujets seront étayés par les résultats d'études numériques du gaz de Bose relativiste à densité finie.Enfin, nous discuterons du problème de l'application de cette approche aux modèles fermioniques où le problème des signes est généré par le déterminant fermionique à valeurs complexes. En tant qu'application spécifique, nous étudierons le modèle Thirring dans deux représentations différentes abordant les défis associés

Extracting small signals from highly oscillating data : the sign problem in particle systems

Les simulations de Monte Carlo sont la méthode numérique de choix pour l'étude des théories des champs sur réseau dans un système non perturbatif. Au fil des ans, les méthodes de Monte Carlo dans les théories de champ sur réseau ont atteint un niveau de maturité tel que dans plusieurs applications QCD, elles fournissent les prédictions les plus fiables pour le comportement à basse énergie de la théorie. Cependant, pour de nombreuses théories intéressantes, une action à valeurs complexes empêche l'utilisation de techniques d'échantillonnage standard. Ceci est généralement connu sous le nom de problème de signe et est présent si le poids de Boltzmann associé aux configurations de champ est non positif ou non réel. Une classe de modèles présentant cette propriété sont les théories de densité finie. Celles-ci seront notre principal intérêt.Dans ce travail, nous nous concentrerons sur l'approche de la densité d'états au problème de signe. Il s'agit d'une technique numérique qui permet d'utiliser les techniques standards de Monte Carlo pour évaluer la densité d'états relatifs à la partie imaginaire de l'action. En faisant cela, le problème du signe est réduit à une intégrale oscillatoire unidimensionnelle plus simple, qui se prête aux méthodes de quadrature déterministes standard.Au cœur de notre implémentation de la méthode de la densité des états se trouve l'algorithme LLR. Nous présenterons la mise en œuvre générale et les développements récents concernant le contrôle des sources possibles de biais. Ensuite, nous étendrons la formulation actuelle pour permettre l'évaluation d'observables génériques. Ces deux sujets seront étayés par les résultats d'études numériques du gaz de Bose relativiste à densité finie.Enfin, nous discuterons du problème de l'application de cette approche aux modèles fermioniques où le problème des signes est généré par le déterminant fermionique à valeurs complexes. En tant qu'application spécifique, nous étudierons le modèle Thirring dans deux représentations différentes abordant les défis associés.Monte Carlo simulations are the numerical method of choice for the study of lattice field theories in a non-perturbative framework. Over the years, Monte Carlo methods in Lattice Field Theories have reached a level of maturity such that in several QCD applications they provide the most reliable predictions for the low-energy behaviour of the theory. However, for many interesting theories, a complex-valued action prevents the use of standard sampling techniques. This is generally known as the sign problem and is present if the Boltzmann weight associated with the field configurations is either non-positive or non-real. A class of models exhibiting this property are finite density theories. These are going to be our primary interest.In this work, we shall focus on the density of states approach to the sign problem. This is a numerical technique that enables us to use standard Monte Carlo techniques to evaluate the density of states relating to the imaginary part of the action. By doing this, the sign problem is reduced to a simpler one-dimensional oscillatory integral, amenable to standard deterministic quadrature methods.At the core of our implementation of the density of states method is the LLR algorithm. We will present the general implementation and recent developments regarding on the control of possible sources of bias. Then we will extend the current formulation to allow for the evaluation of generic observables. Both these topics will be supported by results from numerical studies of the relativistic Bose gas at finite density.Lastly, we will discuss the problem of applying this approach to fermionic models where the sign problem is generated by the complex-valued fermionic determinant. As a specific application, we will study the Thirring model in two different representations discussing the related challenges

Obtenir des signaux petits à partir des données oscillantes : le problème de signe dans les systèmes de particules

Monte Carlo simulations are the numerical method of choice for the study of lattice field theories in a non-perturbative framework. Over the years, Monte Carlo methods in Lattice Field Theories have reached a level of maturity such that in several QCD applications they provide the most reliable predictions for the low-energy behaviour of the theory. However, for many interesting theories, a complex-valued action prevents the use of standard sampling techniques. This is generally known as the sign problem and is present if the Boltzmann weight associated with the field configurations is either non-positive or non-real. A class of models exhibiting this property are finite density theories. These are going to be our primary interest.In this work, we shall focus on the density of states approach to the sign problem. This is a numerical technique that enables us to use standard Monte Carlo techniques to evaluate the density of states relating to the imaginary part of the action. By doing this, the sign problem is reduced to a simpler one-dimensional oscillatory integral, amenable to standard deterministic quadrature methods.At the core of our implementation of the density of states method is the LLR algorithm. We will present the general implementation and recent developments regarding on the control of possible sources of bias. Then we will extend the current formulation to allow for the evaluation of generic observables. Both these topics will be supported by results from numerical studies of the relativistic Bose gas at finite density.Lastly, we will discuss the problem of applying this approach to fermionic models where the sign problem is generated by the complex-valued fermionic determinant. As a specific application, we will study the Thirring model in two different representations discussing the related challenges.Les simulations de Monte Carlo sont la méthode numérique de choix pour l'étude des théories des champs sur réseau dans un système non perturbatif. Au fil des ans, les méthodes de Monte Carlo dans les théories de champ sur réseau ont atteint un niveau de maturité tel que dans plusieurs applications QCD, elles fournissent les prédictions les plus fiables pour le comportement à basse énergie de la théorie. Cependant, pour de nombreuses théories intéressantes, une action à valeurs complexes empêche l'utilisation de techniques d'échantillonnage standard. Ceci est généralement connu sous le nom de problème de signe et est présent si le poids de Boltzmann associé aux configurations de champ est non positif ou non réel. Une classe de modèles présentant cette propriété sont les théories de densité finie. Celles-ci seront notre principal intérêt.Dans ce travail, nous nous concentrerons sur l'approche de la densité d'états au problème de signe. Il s'agit d'une technique numérique qui permet d'utiliser les techniques standards de Monte Carlo pour évaluer la densité d'états relatifs à la partie imaginaire de l'action. En faisant cela, le problème du signe est réduit à une intégrale oscillatoire unidimensionnelle plus simple, qui se prête aux méthodes de quadrature déterministes standard.Au cœur de notre implémentation de la méthode de la densité des états se trouve l'algorithme LLR. Nous présenterons la mise en œuvre générale et les développements récents concernant le contrôle des sources possibles de biais. Ensuite, nous étendrons la formulation actuelle pour permettre l'évaluation d'observables génériques. Ces deux sujets seront étayés par les résultats d'études numériques du gaz de Bose relativiste à densité finie.Enfin, nous discuterons du problème de l'application de cette approche aux modèles fermioniques où le problème des signes est généré par le déterminant fermionique à valeurs complexes. En tant qu'application spécifique, nous étudierons le modèle Thirring dans deux représentations différentes abordant les défis associés

The density of state approach to the sign problem

International audienceApproaches to the sign problem based on the density of states have been recently revived by the introduction of the LLR algorithm, which allows us to compute the density of states itself with exponential error reduction. In this work, after a review of the generalities of the method, we show recent results for the Bose gas in four dimensions, focussing on the identification of possible systematic errors and on methods of controlling the bias they can introduce in the calculation

LapH interpolating fields with open boundary conditions

The stochastic Laplacian Heaviside (LapH) method has proven to be successful in hadronic calculations. In this work, with charm--light spectroscopy in mind, we set up and optimise the LapH procedure limiting ourselves to the evaluation of two--point mesonic correlation functions. The calculations are performed on CLS ensembles with $N_f=2+1$ Wilson-Clover fermions on a $32^3\times64$ lattice with open boundary conditions. We analyse the interplay between the LapH parameters and the boundary effects, and implement a fitting procedure to isolate excitations coming from the border.The stochastic Laplacian Heaviside (LapH) method has proven to be successful in hadronic calculations. In this work, with charm-light spectroscopy in mind, we set up and optimise the LapH procedure limiting ourselves to the evaluation of two-point mesonic correlation functions. The calculations are performed on CLS ensembles with $N_f=2+1$ Wilson-Clover fermions on a $32^3\times64$ lattice with open boundary conditions. We analyse the interplay between the LapH parameters and the boundary effects, and implement a fitting procedure to isolate excitations coming from the border

Mortality after surgery in Europe: a 7 day cohort study

Background: Clinical outcomes after major surgery are poorly described at the national level. Evidence of heterogeneity between hospitals and health-care systems suggests potential to improve care for patients but this potential remains unconfirmed. The European Surgical Outcomes Study was an international study designed to assess outcomes after non-cardiac surgery in Europe.Methods: We did this 7 day cohort study between April 4 and April 11, 2011. We collected data describing consecutive patients aged 16 years and older undergoing inpatient non-cardiac surgery in 498 hospitals across 28 European nations. Patients were followed up for a maximum of 60 days. The primary endpoint was in-hospital mortality. Secondary outcome measures were duration of hospital stay and admission to critical care. We used χ² and Fisher’s exact tests to compare categorical variables and the t test or the Mann-Whitney U test to compare continuous variables. Significance was set at p<0·05. We constructed multilevel logistic regression models to adjust for the differences in mortality rates between countries.Findings: We included 46 539 patients, of whom 1855 (4%) died before hospital discharge. 3599 (8%) patients were admitted to critical care after surgery with a median length of stay of 1·2 days (IQR 0·9–3·6). 1358 (73%) patients who died were not admitted to critical care at any stage after surgery. Crude mortality rates varied widely between countries (from 1·2% [95% CI 0·0–3·0] for Iceland to 21·5% [16·9–26·2] for Latvia). After adjustment for confounding variables, important differences remained between countries when compared with the UK, the country with the largest dataset (OR range from 0·44 [95% CI 0·19 1·05; p=0·06] for Finland to 6·92 [2·37–20·27; p=0·0004] for Poland).Interpretation: The mortality rate for patients undergoing inpatient non-cardiac surgery was higher than anticipated. Variations in mortality between countries suggest the need for national and international strategies to improve care for this group of patients.Funding: European Society of Intensive Care Medicine, European Society of Anaesthesiology