scholarly journals Topological sampling through windings

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 .

scholarly journals Testing algorithms for critical slowing down

2018 ◽  
Vol 175 ◽  
pp. 02008 ◽  
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.

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

scholarly journals Berezinskii-Kosterlitz-Thouless phase transition from lattice sine-Gordon model

2018 ◽  
Vol 175 ◽  
pp. 14003
Author(s):  
Joel Giedt ◽  
James Flamino
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Temperature ◽  
Finite Size ◽  
Monte Carlo Algorithm ◽  
Finite Size Scaling ◽  
Hybrid Monte Carlo ◽  
Lattice Field ◽  
Autocorrelation Time ◽  
Sine Gordon Model

We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory based autocorrelation time, as well as the finite size scaling of the “thickness” observable used in an earlier lattice study by Hasenbusch et al.

scholarly journals On the continuum limit of gauge-fixed compact U(1) lattice gauge theory

2004 ◽  
Vol 580 (3-4) ◽  
pp. 209-215 ◽  
Author(s):  
Subhasish Basak ◽  
Asit K De ◽  
Tilak Sinha
Keyword(s):  
Gauge Theory ◽  
Continuum Limit ◽  
Lattice Gauge Theory ◽  
Lattice Gauge ◽  
The Continuum

scholarly journals Lattice gauge theory and gluon color-confinement in curved spacetime

2015 ◽  
Vol 30 (05) ◽  
pp. 1550020 ◽  
Author(s):  
Kristian Hauser Villegas ◽  
Jose Perico Esguerra
Keyword(s):  
Gauge Theory ◽  
Continuum Limit ◽  
Lattice Gauge Theory ◽  
Covariant Form ◽  
Curved Spacetime ◽  
Color Confinement ◽  
Lattice Gauge ◽  
Frw Metric ◽  
Generally Covariant ◽  
The Continuum

The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman–Robertson–Walker (FRW) metric. Last, we discussed possible future numerical implementation of lattice QCD in curved spacetime.

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