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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Phase transitions in a multistate majority-vote model on complex networks.

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The p-state majority-vote (MV) model transitions from second-order to first-order phase transitions for p≥3. This study explores these order-disorder transitions on complex networks using simulations and theory.

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Area of Science:

  • Statistical physics
  • Complex networks analysis
  • Phase transitions

Background:

  • The two-state majority-vote (MV) model exhibits continuous second-order phase transitions.
  • Understanding phase transitions in generalized models is crucial for complex systems.

Purpose of the Study:

  • Generalize the majority-vote (MV) model to an arbitrary p-state system.
  • Investigate the order-disorder phase transitions in the p-state MV model on complex networks.
  • Analyze the impact of modified dynamics on phase transition order.

Main Methods:

  • Extensive Monte Carlo simulations
  • Mean-field theory
  • Analysis of modified dynamics

Main Results:

  • For p≥3, the p-state MV model exhibits a discontinuous first-order phase transition, unlike the two-state model.
  • Hysteresis phenomena and coexistence of ordered/disordered phases are observed for p≥3.
  • The order of phase transition in the three-state MV model depends on network degree heterogeneity.
  • For p≥4, both original and modified dynamics result in first-order phase transitions.

Conclusions:

  • The generalization of the MV model to p states significantly alters the nature of phase transitions.
  • Network properties, like degree heterogeneity, influence phase transition behavior in multi-state models.
  • First-order phase transitions become prevalent in the p-state MV model for p≥3.