Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ${\varphi }^4$-Model: Autocorrelations and Interface Tension

Abstract

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar ${\varphi }^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.

49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as uuencoded compressed tar file

References in corpus (7)

• Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state Potts Model, and an Estimate for 4d SU(3) Gauge Theory
• Observation of FSS for a First Order Phase Transition
• Multicanonical Cluster Algorithm and the 2-D 7-State Potts Model
• Multicanonical Multigrid Monte Carlo
• Cluster dynamics for first-order phase transitions in the Potts model
• Kinematics of Multigrid Monte Carlo
• Multicanonical study of $D=2$ $O(3)$ nonlinear $\sigma$-model

Cited by in corpus (9)

• Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
• Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles
• Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model
• Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $\sigma$-Models
• Multicanonical Hybrid Monte Carlo: Boosting Simulations of Compact QED
• Multigrid Method versus Staging Algorithm for PIMC Simulations
• Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear $\sigma$-Model
• Exploring the worldline formulation of the Potts model
• Dynamical Critical Properties of the Random-Bond three-state Potts Model