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This study presents an exact solution for a minimal spin model exhibiting a hybrid phase transition. The model, derived from a biased random walk, features a triple point with mixed-order characteristics.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Phase transitions are fundamental in understanding material properties.
  • Hybrid phase transitions exhibit characteristics of both first-order and second-order transitions.

Purpose of the Study:

  • To exactly solve a minimal spin model with a hybrid phase transition.
  • To analyze the phase diagram and identify the characteristics of the hybrid transition.

Main Methods:

  • The study employs the grand canonical ensemble for exact solutions.
  • A diffusion-based model is developed, linked to a biased random walk dynamic.

Main Results:

  • The phase diagram reveals a triple point with hallmarks of a hybrid transition.
  • Discontinuity in average magnetization and algebraically diverging susceptibilities are observed.
  • Two second-order transition curves meet a first-order curve at the triple point.

Conclusions:

  • The model provides a prototypical example of mixed-order behavior in phase transitions.
  • The diffusion-based approach offers a novel perspective on equilibrium statistical mechanics.