Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction.

@article{Horita2016UpperAL,
  title={Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction.},
  author={Toshiki Horita and Hidemaro Suwa and Synge Todo},
  journal={Physical review. E},
  year={2016},
  volume={95 1-1},
  pages={
          012143
        }
}
We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, J_{ij}=|r[over ⃗]_{i}-r[over ⃗]_{j}|^{-(d+σ)}, where d (=2) is the dimension of the system and σ is the decay exponent, by means of the order-N cluster-algorithm Monte Carlo method. In particular, we focus on the upper and lower critical decay exponents, the boundaries between the mean-field-universality… 

Figures and Tables from this paper

Zero-temperature coarsening in the two-dimensional long-range Ising model.

It is found that the growth exponent α≈3/4 is independent of σ and different from α=1/2, as expected for nearest-neighbor models, and this relation for all σ studied is confirmed, reinforcing its general validity.

Zero-Temperature Coarsening in the 2D Long-Range Ising Model

We investigate the nonequilibrium dynamics following a quench to zero temperature of the Ising model with power-law decaying long-range interactions $\propto 1/r^{d+\sigma}$ in $d=2$ spatial

Singular dynamics and emergence of nonlocality in long-range quantum models

We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings

Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions

Abstract The quantum Ising chain with the interaction decaying as a power law 1∕r1+σ of the distance between spins r was investigated numerically. A particular attention was paid to the low-energy

Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field

Bootstrapping the long-range Ising model in three dimensions

  • C. Behan
  • Physics, Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2019
The 3D Ising model and the generalized free scalar of dimension at least 0.75 belong to a continuous line of nonlocal fixed points, each referred to as a long-range Ising model. They can be

Quantum criticality of the transverse-field Ising model with long-range interactions on triangular-lattice cylinders

To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate the ground-state phase diagram of the

Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions.

This work investigates the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice and finds that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents.

Berezinskii-Kosterlitz-Thouless Phase Transitions with Long-Range Couplings.

This Letter considers the effect of long-range decaying couplings ∼r^{-2-σ} on the Berezinskii-Kosterlitz-Thouless transition and discusses the phase diagram, which is far richer than the corresponding short-range one.

Criticality and phase diagram of quantum long-range O( N ) models

Several recent experiments in atomic, molecular and optical systems motivated a huge interest in the study of quantum long-range %spin systems. Our goal in this paper is to present a general

References

SHOWING 1-10 OF 25 REFERENCES

A Guide to Monte Carlo Simulations in Statistical Physics

This chapter discusses Monte Carlo simulations at the periphery of physics and beyond, as well as other methods of computer simulation, and Monte Carlo studies of biological molecules.

Phys

  • Rev. B 8, 281
  • 1973

Phys

  • Rev. Lett. 29, 917
  • 1972

Phys

  • Rev. Lett. 89, 025703
  • 2002

Computer Simulation

Proc

  • Phys. Soc. 67, 233
  • 1954

Phys

  • Rev. E 89, 062120
  • 2014

Europhys

  • Lett. 101, 56003
  • 2013

Proc

  • Int. Conf. Theor. Phys. , 531
  • 1953

Science 336

  • 1416
  • 2012