Nonequilibrium relaxation analysis for first-order phase transitions

Ozeki, Yukiyasu; Kasono, Katsumi; Ito, Nobuyasu; Miyashita, Seiji

doi:10.1016/s0378-4371(02)01788-0

Cited by 32 publications

(41 citation statements)

References 19 publications

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“…In particular, to minimize the hysteresis associated with first-order transitions, we used mixed initial conditions in which different parts of the system are assigned different ordered or disordered states. 33 Where the acceptance rate in MC updates becomes extremely slow, we used the exchange MC method, 34 to avoid local spin freezing at low temperatures. Results are divided into five bins to estimate statistical errors by variance of average values in the bins.…”

Section: A Collinear Nematic Phase For H =0mentioning

confidence: 99%

Nematic, vector-multipole, and plateau-liquid states in the classicalO(3)pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

2010

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The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Néel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r Շ c ϳ 1 / ͱ T, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Néel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be resolved by a proper understanding of way in which long-range Néel order emerges out of well-formed local correlations and identify nematic and vector-multipole orders hidden in the different Coulomb phases of the model. So far as experiment is concerned, our results suggest that where long-range interactions are unimportant, the magnetic properties of Cr spinels which exhibit half-magnetization plateaux may be largely independent of the type of magnetic order present.

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Section: A Collinear Nematic Phase For H =0mentioning

confidence: 99%

Nematic, vector-multipole, and plateau-liquid states in the classicalO(3)pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

2010

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“…Data collapse of the correlation function C(x,t) of the 2D dynamic XY model with a disordered start. Solid lines are for tϭ20, 40,80,160,320,640,1280,2560,5120, and 10 240 ͑from left͒. Circles, squares, diamonds, triangles up, triangles left, triangles down, triangles right, pluses, and crosses fitted to the curve of tϭ160 are curves of tϭ20, 40,80,320,640,1280,2560,5120 and 10 240, but rescaled according to Eq.…”

Section: B Quench With Disordered Start For Xy Modelmentioning

confidence: 99%

“…Solid lines are for tϭ20, 40,80,160,320,640,1280,2560,5120, and 10 240 ͑from left͒. Circles, squares, diamonds, triangles up, triangles left, triangles down, triangles right, pluses, and crosses fitted to the curve of tϭ160 are curves of tϭ20, 40,80,320,640,1280,2560,5120 and 10 240, but rescaled according to Eq. ͑15͒ with zϭ2.01, In Table II, the dynamic exponent z extracted from A(t), M (2) (t), and M (m 0 ,t) is given.…”

Section: B Quench With Disordered Start For Xy Modelmentioning

confidence: 99%

Corrections to scaling in two-dimensional dynamicXYand fully frustratedXYmodels

Zheng

Ren

2003

Phys. Rev. E

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With large-scale Monte Carlo simulations, we investigate the two-dimensional dynamic XY and fully frustrated XY models. Dynamic relaxation starting from a disordered or an ordered state is carefully analyzed. It is confirmed that there is a logarithmic correction to scaling for a disordered start, but a power-law correction for an ordered start. Rather accurate values of the static exponent eta and the dynamic exponent z are estimated.

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“…Next, the system is studied via nonequilibrium relaxation method [25] that is an efficient tool of analysis of equilibrium phase transitions. The numerical results are shown in Fig.6.…”

Section: Simulation Resultsmentioning

confidence: 99%

The critical properties of the agent-based model with environmental–economic interactions

Kuscsik

Horváth

Gmitra

2007

Physica A: Statistical Mechanics and its Applications

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The steady-state and nonequilibrium properties of the model of environmentaleconomic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model possess the discontinuous transition between the safe and catastrophic ecology. Right at the critical line, the broad-scale power-law distributions of emission rates have been identified. Their relationship to Zipf's law and models of self-organized criticality is discussed.

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Nonequilibrium relaxation analysis for first-order phase transitions

Cited by 32 publications

References 19 publications

Nematic, vector-multipole, and plateau-liquid states in the classicalO(3)pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

Nematic, vector-multipole, and plateau-liquid states in the classicalO(3)pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

Corrections to scaling in two-dimensional dynamicXYand fully frustratedXYmodels

The critical properties of the agent-based model with environmental–economic interactions

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