High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model.

@article{Xu2020HighresolutionMC,
  title={High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model.},
  author={Jiahao Xu and Alan M. Ferrenberg and David P. Landau},
  journal={Physical review. E},
  year={2020},
  volume={101 2-1},
  pages={
          023315
        }
}
We apply extensive Monte Carlo simulations to study the probability distribution P(m) of the order parameter m for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the Wolff cluster flipping algorithm, and histogram reweighting together with finite-size scaling analyses are then used to extract a precise functional form for the probability distribution of the magnetization, P(m), in the thermodynamic limit. This form should serve… 

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References

SHOWING 1-10 OF 29 REFERENCES

Probability distribution of the order parameter for the three-dimensional ising-model universality class: A high-precision monte carlo study

  • TsypinBloté
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
The probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point is studied, and a simple, but remarkably accurate, approximate formula is obtained describing the universal shape of P( M).

Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model.

The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations, and clear numerical evidence for "fat" stretched exponential tails exists below thecritical temperature, indicating the possible presence of fat tails at the critical temperature.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model.

This work has investigated the critical behavior of the simple cubic Ising Model, using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic.

Finite size scaling study of lattice models in the three-dimensional Ising universality class

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up

Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?

Critical finite-size scaling functions for the order-parameter distribution of the two- and three-dimensional Ising model are investigated. Within a recently introduced classification theory of phase

Ising universality in three dimensions: a Monte Carlo study

We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbour interactions, a

Finite size scaling analysis of ising model block distribution functions

The distribution functionPL(s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is

Critical-point and coexistence-curve properties of the Lennard-Jones fluid: A finite-size scaling study.

  • Wilding
  • Chemistry
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
Monte Carlo simulations within the grand canonical ensemble are used to explore the liquid-vapour coexistence curve and critical point properties of the Lennard-Jones fluid and it is demonstrated that this procedure permits an efficient and accurate mapping of the coexistence Curve, even deep within the two phase region.

Scaling fields and universality of the liquid-gas critical point.

An extensive Monte Carlo study of the density and energy fluctuations in a 2D Lennard-Jones fluid, within the grand-canonical ensemble, incorporating the mixed character of the scaling fields that manifests particle-hole asymmetry.