Tethered Monte Carlo: computing the effective potential without critical slowing down

Abstract

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.

32 pages, 8 eps figures. Corrected Eq. (36), which is wrong in the published paper

References in corpus (28)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Critical Phenomena and Renormalization-Group Theory
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Wang-Landau algorithm for continuous models and joint density of states
• Finite size effects on measures of critical exponents in d=3 O(N) models
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• Finite-Size Scaling at $\xi /L\gg 1$
• Integrable field theory and critical phenomena. The Ising model in a magnetic field
• JANUS: an FPGA-based System for High Performance Scientific Computing
• On the formation/dissolution of equilibrium droplets
• New Universality Class in three dimensions: the Antiferromagnetic $R{P}^2$ model
• Simulating spin systems on IANUS, an FPGA-based computer
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Critical properties of the Antiferromagnetic \RP2$ model in three dimensions
• First order transition in a three dimensional disordered system
• Monte Carlo study of the evaporation/condensation transition on different Ising lattices
• Cluster simulations of loop models on two-dimensional lattices
• The critical equation of state of the 2D Ising model
• Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Critical speeding-up in a local dynamics for the random-cluster model
• Short distance behaviour of correlators in the 2D Ising model in a magnetic field
• Weak first order transition in the three-dimensional site-diluted Ising antiferromagnet in a magnetic field
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning
• Study of the 2d Ising Model with mixed perturbation
• Critical renormalized coupling constants in the symmetric phase of the Ising models

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