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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising

Djordje Spasojević1, Svetislav Mijatović1, Víctor Navas-Portella2

  • 1Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia.

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We studied how 3D systems transition to 2D in the random-field Ising model. Our findings explain critical crossovers and offer new models for analyzing experimental data, especially for thin 3D systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • The random-field Ising model is crucial for understanding magnetic materials.
  • Investigating phase transitions in nonequilibrium systems is a key challenge.
  • Finite-size scaling is essential for interpreting experimental results in finite systems.

Purpose of the Study:

  • To explore the critical crossover from 3D to 2D in the nonequilibrium random-field Ising model.
  • To develop and test bivariate finite-size scaling hypotheses for L×L×l systems.
  • To propose a model for effective critical disorder and analyze avalanche distributions.

Main Methods:

  • Extensive numerical simulations of the random-field Ising model.
  • Application of bivariate finite-size scaling techniques.
  • Development of a model for effective critical disorder (R_{c}^{eff}(l,L)).

Main Results:

  • Bivariate finite-size scaling hypotheses were established, explaining the size-driven crossover.
  • A model for effective critical disorder was proposed with a unique fitting parameter.
  • Expressions for the scaling of avalanche distributions were derived.

Conclusions:

  • The study provides a framework for understanding dimensional crossovers in magnetic systems.
  • The proposed model simplifies analysis of experimental data, particularly for thin 3D systems.
  • The findings have implications for materials science and statistical physics research.