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

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.

• Publication year

  2008

• Venue

  Nuclear Physics

• Publication date

  2008-06-03

• Fields of study

  Physics

• Identifiers
  DOI 10.1016/j.nuclphysb.2008.07.009 10.1016/j.nuclphysb.2009.04.022arXiv 0806.0543
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Lattice gauge theories: an introduction

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  2007cited by this paper
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  2007cited by this paper
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  2004cited by this paper
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  2004cited by this paper
• Dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model

  2004cited by this paper
• Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes

  2003cited by this paper
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  2002cited by this paper
• Study of the 2d Ising model with mixed perturbation

  2002cited by this paper
• Numerical recipes in C

  2002cited by this paper
• Metastable liquids

  2002influential reference
• Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy

  2001cited by this paper
• The intrinsic coupling in integrable quantum field theories

  2000cited by this paper
• The critical equation of state of the 2-D ising model

  2000cited by this paper
• Critical phenomena and renormalization-group theory

  2000cited by this paper
• Efficient, multiple-range random walk algorithm to calculate the density of states.

  2000cited by this paper
• Monte Carlo Methods in Statistical Physics

  1999cited by this paper
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

  1999cited by this paper
• Short distance behaviour of correlators in the 2d Ising model in a magnetic field

  1999cited by this paper
• Critical renormalized coupling constants in the symmetric phase of the Ising models

  1999cited by this paper
• Functional integration : basics and applications

  1997cited by this paper
• Theory of protein folding: the energy landscape perspective.

  1997cited by this paper
• Spin glasses and random fields

  1997cited by this paper
• Critical properties of the antiferromagnetic RP 2 model in three dimensions

  1996cited by this paper
• Finite size effects on measures of critical exponents in d=3 O(N) models

  1996cited by this paper
• NON-INTEGRABLE QUANTUM FIELD THEORIES AS PERTURBATIONS OF CERTAIN INTEGRABLE MODELS

  1996cited by this paper
• New universality class in three dimensions?: the antiferromagnetic RP2 model

  1995cited by this paper
• Finite-Size Scaling at $\xi/L \gg 1$

  1994cited by this paper
• Spin glasses : an experimental introduction

  1993influential reference
• Multicanonical ensemble: A new approach to simulate first-order phase transitions.

  1992cited by this paper
• Collective Monte Carlo updating for spin systems.

  1989cited by this paper
• Critical dynamics and global conservation laws.

  1989cited by this paper
• Integrals of Motion and S-Matrix of the (scaled) T = T c Ising Model with Magnetic Field

  1989cited by this paper
• Monte Carlo simulations in statistical physics

  1988cited by this paper
• Monte Carlo simulation of a lattice field theory as correlated percolation

  1988cited by this paper
• Spin Glass Theory and Beyond

  1987cited by this paper
• Nonuniversal critical dynamics in Monte Carlo simulations.

  1987cited by this paper
• Effects of the random number generator on computer simulations

  1985cited by this paper
• Quarks, Gluons and Lattices

  1984cited by this paper
• Field Theory, the Renormalization Group and Critical Phenomena

  1984cited by this paper
• Microcanonical Monte Carlo Simulation

  1983cited by this paper
• Monte Carlo study of weighted percolation clusters relevant to the Potts models

  1983cited by this paper
• Solving φ1,24 field theory with Monte Carlo

  1982cited by this paper
• Field theory

  1979influential reference
• Bounded and Inhomogeneous Ising Models. I. Specific-Heat Anomaly of a Finite Lattice

  1969cited by this paper
• Diffusion Constants near the Critical Point for Time-Dependent Ising Models. I

  1966cited by this paper
• Equation of State Calculations by Fast Computing Machines

  1953cited by this paper
• The Spontaneous Magnetization of a Two-Dimensional Ising Model

  1952cited by this paper
• Crystal statistics. I. A two-dimensional model with an order-disorder transition

  1944cited by this paper

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• Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling

  2022cites this paper
• Statistical mechanics of coupled supercooled liquids in finite dimensions

  2021cites this paper
• Random-field Ising model criticality in a glass-forming liquid.

  2020cites this paper
• An Ising model for metal-organic frameworks.

  2017cites this paper
• Heisenberg Spin Glass with Random Exchange Anisotropy

  2016cites this paper
• An Introduction to Spin Glasses: History, Simulations and Phase Transition

  2016cites this paper
• On the inner workings of Monte Carlo codes

  2013influential citation
• On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory

  2012cites this paper
• Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

  2011cites this paper
• Nature of the spin-glass phase at experimental length scales

  2010cites this paper
• Static versus dynamic heterogeneities in the D = 3 Edwards-Anderson-Ising spin glass.

  2010cites this paper
• Cluster Monte Carlo algorithm with a conserved order parameter.

  2009cites this paper
• Mean-value identities as an opportunity for Monte Carlo error reduction.

  2009cites this paper