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Rutas fractales de búsqueda en profundidad en modelos de física estadística

Qiyuan Shi1, Youjin Deng1,2,3, Ming Li4

  • 1University of Science and Technology of China, Department of Modern Physics, Hefei, Anhui 230026, China.

Physical review. E
|December 23, 2025
PubMed
Resumen

Las rutas de búsqueda en profundidad (DFS) revelan propiedades fractales en modelos de física estadística. Esta sonda geométrica ofrece nuevas perspectivas sobre fenómenos críticos más allá de los métodos tradicionales.

Palabras clave:
búsqueda en profundidadfractalesfísica estadísticafenómenos críticosmodelos de bucle O(n)percolacióndimensión fractalsondas geométricas

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Área de la Ciencia:

  • Física Estadística
  • Sistemas Complejos
  • Sondas Geométricas

Sus antecedentes:

  • Las propiedades fractales son cruciales para comprender los fenómenos críticos.
  • Los observables tradicionales pueden no capturar completamente los comportamientos de sistemas complejos.

Objetivo del estudio:

  • Investigar las características fractales de las rutas de búsqueda en profundidad (DFS).
  • Explorar las rutas DFS en configuraciones críticas de modelos de física estadística.
  • Evaluar DFS como una nueva sonda geométrica para fenómenos críticos.

Principales métodos:

  • Análisis de rutas DFS en el modelo de bucle O(n) 2D y percolación de enlaces.
  • Examen a través de varias dimensiones (d=2 a 6) y regímenes críticos.
  • Cálculo de las dimensiones fractales para las rutas DFS.

Principales resultados:

  • Las rutas DFS exhiben una dimensión fractal constante d_{DFS}=1+g/8 en el modelo de bucle O(n).
  • Se observa un escalado fractal no trivial de las rutas DFS en la percolación de enlaces a través de dimensiones.
  • Las rutas DFS muestran un comportamiento fractal en redes 2D y se vuelven de relleno de espacio en dimensiones superiores.

Conclusiones:

  • La búsqueda en profundidad (DFS) proporciona una sonda geométrica robusta para fenómenos críticos.
  • El análisis de rutas DFS ofrece información más allá de los observables tradicionales en física estadística.
  • La naturaleza fractal de las rutas DFS es un hallazgo significativo para la investigación de sistemas complejos.