Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization

We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As examples of such universality, we present the large N solutions of two prototype models for XQCD, in which the mass of the spurious pion and sigma resonance go to infinity with the cut-off. Even if the universality conjecture turns out to be false, we believe that XQCD will still be useful as a low energy effective action for QCD phenomenology on the lattice. Numerical simulations are recommended to further investigate the possible benefits of XQCD in extracting QCD predictions.

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Testing algorithms for critical slowing down

EPJ Web of Conferences ◽

10.1051/epjconf/201817502008 ◽

2018 ◽

Vol 175 ◽

pp. 02008 ◽

Cited By ~ 3

Author(s):

Guido Cossu ◽

Peter Boyle ◽

Norman Christ ◽

Chulwoo Jung ◽

Andreas Jüttner ◽

...

Keyword(s):

Monte Carlo ◽

Topological Charge ◽

Continuum Limit ◽

Critical Slowing Down ◽

Gauge Fields ◽

Hybrid Monte Carlo ◽

Slowing Down ◽

Testing Algorithms ◽

New Algorithms ◽

The Continuum

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

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From Atomistic to Continuum Descriptions of Morphological Evolution

MRS Proceedings ◽

10.1557/proc-859-jj8.8 ◽

2004 ◽

Vol 859 ◽

Author(s):

Christoph A. Haselwandter ◽

Dimitri D. Vvedensky

Keyword(s):

Monte Carlo ◽

Continuum Limit ◽

Growth Models ◽

Kinetic Monte Carlo ◽

Morphological Evolution ◽

Strain Relaxation ◽

Direct Analysis ◽

Langevin Equations ◽

Kinetic Monte Carlo Simulations ◽

The Continuum

ABSTRACTLattice Langevin equations are derived from the rules of lattice growth models. These provide an exact mathematical description that is suitable for direct analysis, such as the passage to the continuum limit, as well as a computational alternative to kinetic Monte Carlo simulations. This approach is applied to ballistic deposition and a model for conditional deposition, both of which yield the Kardar–Parisi– Zhang equation in the continuum limit, and a model of strain relaxation during heteroepitaxy.

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Testing a non-perturbative mechanism for elementary fermion mass generation: numerical results

EPJ Web of Conferences ◽

10.1051/epjconf/201817508008 ◽

2018 ◽

Vol 175 ◽

pp. 08008 ◽

Cited By ~ 2

Author(s):

Stefano Capitani ◽

Giulia Maria De Divitiis ◽

Petros Dimopoulos ◽

Roberto Frezzotti ◽

Marco Garofalo ◽

...

Keyword(s):

Elementary Particle ◽

Continuum Limit ◽

Scalar Fields ◽

Higgs Mechanism ◽

Numerical Results ◽

Fermion Mass ◽

Recent Proposal ◽

Mass Generation ◽

Complex Scalar ◽

The Continuum

Based on a recent proposal according to which elementary particle masses could be generated by a non-perturbative dynamical phenomenon, alternative to the Higgs mechanism, we carry out lattice simulations of a model where a non-abelian strongly interacting fermion doublet is also coupled to a doublet of complex scalar fields via a Yukawa and an “irrelevant" Wilson-like term. In this pioneering study we use naive fermions and work in the quenched approximation. We present preliminary numerical results both in the Wigner and in the Nambu-Goldstone phase, focusing on the observables relevant to check the occurrence of the conjectured dynamical fermion mass generation effect in the continuum limit of the critical theory in its spontaneously broken phase.

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A MONTE CARLO STUDY OF THE O(3) σ-MODEL ON A CURVED RANDOM SURFACE

Modern Physics Letters A ◽

10.1142/s0217732389000575 ◽

1989 ◽

Vol 04 (05) ◽

pp. 475-481 ◽

Cited By ~ 2

Author(s):

HIROSHI KOIBUCHI ◽

MITSURU YAMADA

Keyword(s):

Monte Carlo ◽

Magnetic Susceptibility ◽

Specific Heat ◽

Continuum Limit ◽

Pair Correlation ◽

Monte Carlo Study ◽

Link Length ◽

Random Surface ◽

Random Lattice ◽

The Continuum

The O(3) σ-model is studied numerically on a curved random surface, which is constructed from a flat random lattice by the change of each link length. The pair correlation, the specific heat and the magnetic susceptibility are calculated. It is shown that the continuum limit of the model can be obtained when the curvature is reasonably small.

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RISE OF THE CENTRIST: FROM BINARY TO CONTINUOUS OPINION DYNAMICS

International Journal of Modern Physics C ◽

10.1142/s0129183108013023 ◽

2008 ◽

Vol 19 (09) ◽

pp. 1459-1475 ◽

Cited By ~ 1

Author(s):

GEORGE A. BAKER ◽

JAMES P. HAGUE

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Continuum Limit ◽

Linear Chain ◽

Opinion Dynamics ◽

Memory Effects ◽

Time Step ◽

Binary Model ◽

Long Time ◽

The Continuum

We propose a model that extends the binary "united we stand, divided we fall" opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions on a linear chain. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.

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Topological sampling through windings

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09677-6 ◽

2021 ◽

Vol 81 (10) ◽

Author(s):

David Albandea ◽

Pilar Hernández ◽

Alberto Ramos ◽

Fernando Romero-López

Keyword(s):

Monte Carlo ◽

Gauge Theory ◽

Continuum Limit ◽

Two Dimensional ◽

Expectation Values ◽

Hybrid Monte Carlo ◽

Pure Gauge Theory ◽

Fixed Topology ◽

Autocorrelation Time ◽

The Continuum

AbstractWe propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

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