An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems

@article{Watanabe2011AnEM,
  title={An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems},
  author={Kazuya Watanabe and Munetaka Sasaki},
  journal={Journal of the Physical Society of Japan},
  year={2011},
  volume={80},
  pages={093001-093001}
}
We present an efficient Monte-Carlo method for long-range interacting systems to calculate free energy as a function of an order parameter. In this method, a variant of the Wang–Landau method regarding the order parameter is combined with the stochastic cutoff method, which has recently been developed for long-range interacting systems. This method enables us to calculate free energy in long-range interacting systems with reasonable computational time despite the fact that no approximation is… Expand
5 Citations

Figures from this paper

Critical temperature of site-diluted spin-1/2 systems with long-range ferromagnetic interactions
In the paper the Pair Approximation (PA) method for studies of the site-diluted spin-1/2 systems of arbitrary dimensionality with the long-range ferromagnetic interactions is adopted. The methodExpand
Phase transitions, order by disorder, and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice.
TLDR
An analytical and numerical study of the Ising model on a bilayer honeycomb lattice including interlayer frustration and coupling with an external magnetic field and characterize the phase transitions and discuss the phase diagrams. Expand
Thermal stability of the geometrically constrained magnetic wall and its effect on a domain-wall spin valve
We studied thermal fluctuations in magnetoresistance (MR) signals originating from geometrically confined magnetic walls (GCMWs) of nanometer size. To this end, we developed a novel numericalExpand
A Superparamagnetic State Induced by a Spin Reorientation Transition in Ultrathin Magnetic Films
We investigate a spin reorientation transition (SRT) in ultrathin magnetic films by Monte-Carlo simulations. We assume that the lateral size of the film is relatively small and it has a single-domainExpand
Role of atomic-scale thermal fluctuations in the coercivity
The microscopic mechanism of coercivity at finite temperature is a crucial issue for permanent magnets. Here we present the temperature dependence of the coercivity of an atomistic spin model for theExpand

References

SHOWING 1-10 OF 21 REFERENCES
Order-N cluster Monte Carlo method for spin systems with long-range interactions
TLDR
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented that strictly fulfills the detailed balance and the realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm. Expand
MONTE CARLO METHOD FOR SPIN MODELS WITH LONG-RANGE INTERACTIONS
We introduce a Monte Carlo method for the simulation of spin models with ferromagnetic long-range interactions in which the amount of time per spin-flip operation is independent of the system size,Expand
Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram.
  • F. Wang, D. Landau
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
An efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models that overcomes the tunneling barrier between coexisting phases at first-order phase transitions. Expand
Multiple "time step" Monte Carlo simulations: application to charged systems with Ewald summation.
TLDR
The structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of theEwald summation and the common Metropolis Monte Carlo method. Expand
Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions
The N2 computations implicit in the Coulomb and other long range interactions remain the critical bottleneck in atomic‐level simulations of the structure and dynamics of large systems. We report hereExpand
Stochastic potential switching algorithm for Monte Carlo simulations of complex systems.
  • C. Mak
  • Computer Science, Medicine
  • The Journal of chemical physics
  • 2005
TLDR
A new Monte Carlo method based on a novel stochastic potential switching algorithm that produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude is described. Expand
Wang-Landau algorithm for continuous models and joint density of states.
TLDR
A modified Wang-Landau algorithm for models with continuous degrees of freedom is presented and strategies to significantly speed up this calculation for large systems over a large range of energy and order parameter are presented. Expand
Molecular dynamics simulations of proteins in water without the truncation of long-range Coulomb interactions
Abstract A new program package (COSMOS90) for molecular dynamics simulations was developed to simulate large molecular systems consisting of more than tens of thousands of atoms without theExpand
Simulation of an ensemble with varying magnetic field: A numerical determination of the order-order interface tension in the D=2 Ising model.
TLDR
This ensemble where the partition function is simulated with a term in the action containing a varying magnetic field demonstrates on lattices with periodic boundary conditions that it is possible to enhance the appearance of order-order interfaces by many orders of magnitude. Expand
Static critical behavior of three-dimensional classical Heisenberg models: A high-resolution Monte Carlo study.
Using both recently developed cluster-algorithm and histogram methods, we have carried out a highresolution Monte Carlo study of static critical properties of classical ferromagnetic HeisenbergExpand
...
1
2
3
...