Microcanonical Monte Carlo simulations for the two-dimensional XY model

Ota, Smita; Fähnle, M.

doi:10.1088/0953-8984/4/24/011

Cited by 18 publications

(9 citation statements)

References 17 publications

(7 reference statements)

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“…The inflection points of the curves are located close to the transition point h c . It is not surprising that the angular displacements ϑ are a sensitive measure of orientational order in the system: in case of the XY model, at low temperatures, a direct relation between a quantity similar to 1 − ϑ 2 and the magnetization can be established [10,49]. Similar to the temperature considered in earlier studies of the XY model [20], T S is associated with kinetic information contained in the rotational degrees of freedom of the system.…”

Section: Scaling Behavior At Selected Energy Densitiesmentioning

confidence: 84%

Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks

Melchert¹

2022

Preprint

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The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting classical spins, built upon the correspondence between complex-valued modes and two-component spins, are employed to define two-component and singlecomponent order parameters. A comprehensive finite-size scaling analysis is performed to estimate critical points and exponents of a second-order phase transition, driven by the optical energy per mode. Equilibrium properties of the system are compared to exact results whenever applicable. Considering various parameter settings, our results confirm the mean-field nature of the transition and establish the critical line in the nonlinearity-energy-density phase diagram. Critical scaling leads to infer the upper critical dimension dc = 4. Connection to thermodynamic quantities is established by means of a kinetic temperature with appropriate zero-temperature limit. In the low temperature phase (low energy per mode), spins align. In the high temperature phase (large energy per mode), spins rotate independent of one another.

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Section: Scaling Behavior At Selected Energy Densitiesmentioning

confidence: 84%

Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks

Melchert¹

2022

Preprint

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“…We performed micro-canonical Monte Carlo (MC) simulations [49,50] on 30 × 30 rotator system using the Hamiltonian given in Equation (1). There are also other S. OTA, S. B. OTA 141 simulation methods which have been reported recently [51,52].…”

Section: Introductionmentioning

confidence: 99%

Nature of First-Order Transition in Planar Rotator Model with Modified Potential

Ota¹

2013

JMP

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We have carried out micro-canonical Monte Carlosimulations of a planar rotator model in 30 × 30 lattice using periodic boundary conditions. The energy distribution of the rotator in the lattice shows features that can be associated with spin wave and vortex excitations. The results supplement the first-order transition observed in canonicalMonte Carlosimulation, due to vortex nucleation. We also see features that can be associated with the in-homogeneity of vortex charge in the critical region.

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“…Here, the system energy is an input parameter and the temperature is obtained through the simulations. Among the various spin models, this microcanonical MC simulation technique has been applied to the Ising model [8][9][10][11][12][13][14] and the XY -model [15][16][17]. Ergodicity has been demonstrated empirically for these models [10,15].…”

Section: Introductionmentioning

confidence: 99%

“…Among the various spin models, this microcanonical MC simulation technique has been applied to the Ising model [8][9][10][11][12][13][14] and the XY -model [15][16][17]. Ergodicity has been demonstrated empirically for these models [10,15]. The system complexity is expected to give rise to ergodicity.…”

Section: Introductionmentioning

confidence: 99%

Microcanonical Monte Carlo simulations of the first-order transition in the two-dimensional Potts model

Ota

2000

J. Phys.: Condens. Matter

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Microcanonical Monte Carlo simulations have been implemented in the two-dimensional (2D) q -state Potts model. The ergodicity of this simulation technique for the Potts model is studied. It does not seem to depend on the value of q . A lack of ergodicity for small values of the system energy is reported and discussed. It has been found that the temperature dependences of physical quantities exhibit an `S'-shaped nature at the first-order transition. The degree of `S'-shaped nature was enhanced by increasing q and reducing the system size. We believe on the basis of our computer simulations that the `S' shape represents the equilibrium behaviour of a finite isolated system.

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Microcanonical Monte Carlo simulations for the two-dimensional XY model

Cited by 18 publications

References 17 publications

Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks

Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks

Nature of First-Order Transition in Planar Rotator Model with Modified Potential

Microcanonical Monte Carlo simulations of the first-order transition in the two-dimensional Potts model

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