Exploring the worldline formulation of the Potts model
arXiv:1911.12728 · doi:10.1016/j.nuclphysb.2020.115008
Abstract
We revisit the issue of worldline formulations for the q-state Potts model and discuss a worldline representation in arbitrary dimensions which also allows for magnetic terms. For vanishing magnetic field we implement a Hodge decomposition for resolving the constraints with dual variables, which in two dimensions implies self-duality as a simple corollary. We present exploratory 2-d Monte Carlo simulations in terms of the worldlines, based on worm algorithms. We study both, vanishing and non-zero magnetic field, and explore q between q = 2 and q = 30, i.e., Potts models with continuous, as well as strong first order transitions.
arXiv commentDiscussion of statistical errors improved and various comments added. Final version to appear in Nuclear Physics B
References in corpus (16)
- Worm algorithms for classical statistical models
- Solution of the Complex Action Problem in the Potts Model for Dense QCD
- The three-dimensional, three-state Potts Model in an External Field
- The QCD phase diagram according to the center group
- Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
- Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
- Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study
- Worm algorithms for the 3-state Potts model with magnetic field and chemical potential
- Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
- Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
- Potts Flux Tube Model at Nonzero Chemical Potential
- New developments for dual methods in lattice field theory at non-zero density
- Dual Geometric Worm Algorithm for Two-Dimensional Discrete Classical Lattice Models
- Solving the Complex Phase Problem in a QCD Related Model
- Geometric allocation approach to accelerating directed worm algorithm
- Remarks on the construction of worm algorithms for lattice field theories in worldline representation