Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models

Abstract

We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update scheme is proposed. Sample simulations are reported and the method turns out to be similarly efficient as the reflection cluster method, but it has greater potential for systematic generalization to other lattice field theories. A variant action suggested by the method is also simulated and leads to a rather extreme demonstration of the concept of universality of the scaling or continuum limit.

27 pages, 6 figures, 5 tables. The combinatoric derivation of the (unchanged) algorithm is corrected. Independently, all data in sect.5 are revised due to a software error, with unchanged conclusions on universality.

References in corpus (8)

• Trivializing maps, the Wilson flow and the HMC algorithm
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Precision check on triviality of phi^4 theory by a new simulation method
• Logarithmic corrections to O(a^2) lattice artifacts
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations
• Efficient Cluster Algorithm for CP(N-1) Models

Cited by in corpus (37)

• Approaches to the sign problem in lattice field theory
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• A qubit regularization of the $O(3)$ sigma model
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model
• Worm Monte Carlo study of the honeycomb-lattice loop model
• A new dual representation for staggered lattice QCD
• The O(n) loop model on a three-dimensional lattice
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• New developments for dual methods in lattice field theory at non-zero density
• Clock model interpolation and symmetry breaking in O(2) models
• Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model
• The worm process for the Ising model is rapidly mixing
• Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
• A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations
• Testing the event-chain algorithm in asymptotically free models
• Sampling of General Correlators in Worm Algorithm-based Simulations
• Tensor renormalization group study of the 2d O(3) model
• Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model
• Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
• Leaf-excluded percolation in two and three dimensions
• Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• O(3) model with Nienhuis action
• Approximate dual representation for Yang-Mills SU(2) gauge theory
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$
• Graphical Representations and Worm Algorithms for the O($N$) Spin Model
• Comparison between Fermion Bag Approach and Complex Langevin Dynamics for Massive Thirring Model at Finite Density in 0 + 1 Dimensions
• Feasibility of Diagrammatic Monte-Carlo based on weak-coupling expansion in asymptotically free theories: case study of $O(N)$ sigma-model in the large-$N$ limit