Monte Carlo Evaluation of the Continuum Limit of the Two-Point Function of the Euclidean Free Real Scalar Field Subject to Affine Quantization

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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DISCRETE GRAVITY AND ITS CONTINUUM LIMIT

Modern Physics Letters A ◽

10.1142/s0217732305015793 ◽

2005 ◽

Vol 20 (03) ◽

pp. 213-225

Author(s):

YI LING

Keyword(s):

Scalar Field ◽

Cosmological Constant ◽

Continuum Limit ◽

Constant Term ◽

Chaplygin Gas ◽

Fine Tuning ◽

Massless Scalar ◽

Massless Scalar Field ◽

Cosmological Singularity ◽

The Continuum

Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general fashion. However, whether the continuum limit of such discretized theories exists is model dependent. In the case of massless scalar field coupled to gravity with Λ=0, the continuum limit can only be achieved by fine tuning the recurrence constant. We regard this failure as the implication that cosmological constant should vary with time. For this reason we replace the massless scalar field by Chaplygin gas which may contribute an effective cosmological constant term with the evolution of the universe. It turns out that the continuum limit can indeed be reached in this case.

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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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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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New Affine Coherent States Based on Elements of Nonrenormalizable Scalar Field Models

Advances in Mathematical Physics ◽

10.1155/2010/191529 ◽

2010 ◽

Vol 2010 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

John R. Klauder

Keyword(s):

Scalar Field ◽

Ground State ◽

Coherent States ◽

Continuum Limit ◽

Quantum Fields ◽

Commutation Relations ◽

Scalar Field Models ◽

Scalar Quantum ◽

Definition Of ◽

The Continuum

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author's approach to nontrivial formulations of such nonrenormalizable models.

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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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