A Cluster Method for the Ashkin--Teller Model

Abstract

A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent $z$ along the line, following the variation of the ratio $\alpha /\nu$, in a manner which satisfies the Li-Sokal bound $z_{cluster}\ge \alpha /\nu$, that was so far proved only for Potts models.

18 pages, Revtex, figures included

References in corpus (1)

• Cluster Algorithm for Vertex Models

Cited by in corpus (31)

• The Random-Cluster Model
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Phase transitions in the frustrated Ising model on the square lattice
• Entanglement entropy of two disjoint intervals in c=1 theories
• Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study
• Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model
• Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
• Monte Carlo study of very weak first-order transitions in the three-dimensional Ashkin-Teller model
• Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model
• Percolation and cluster Monte Carlo dynamics for spin models
• Random-Cluster Representation of the Ashkin-Teller Model
• Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder
• Thermal valence-bond-solid transition of quantum spins in two dimensions
• Nonequilibrium phase transitions in isotropic Ashkin-Teller Model
• Role of further-neighbor interactions in modulating the critical behavior of the Ising model with frustration
• Critical interfaces and duality in the Ashkin Teller model
• Critical interfaces of the Ashkin-Teller model at the parafermionic point
• The anisotropic Ashkin-Teller model: a renormalization group study
• The Dual Gonihedric 3D Ising Model
• Emergent criticality in fully frustrated quantum magnets
• The conformal anomaly of k-strings
• On the phase diagram of the discrete $Z_6$ spin models
• Critical properties of the Hintermann-Merlini model
• Stability of the Griffiths phase in the 2D Potts model with correlated disorder
• Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models
• Dynamic Critical Behavio(u)r of a Cluster Algorithm for the Ashkin--Teller Model
• Exact relations between damage spreading and thermodynamic functions for the N-color Ashkin-Teller model
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Broadening of the confining flux tube joining higher-representation sources
• Spin interfaces and crossing probabilities of spin clusters in parafermionic models