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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 internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and...
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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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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Entropy-induced phase transitions in a hidden Potts model.

Cook Hyun Kim1, D-S Lee2, B Kahng1

  • 1Center for Complex Systems, KI of Grid Modernization, Korea Institute of Energy Technology, Naju, Jeonnam 58330, Korea.

Physical Review. E
|September 19, 2024
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Summary
This summary is machine-generated.

This study reveals novel supercritical behavior in the q-state Potts model with hidden states. The research details a complex phase diagram with various transitions and critical points, offering new insights into spin systems.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics

Background:

  • Spin systems exhibit entropy contributions from hidden states.
  • The q-state Potts model is a fundamental framework for studying magnetic and other cooperative phenomena.

Purpose of the Study:

  • To explore the phase diagram of the q-state Potts model with additional hidden states.
  • To analytically identify and characterize various phase transitions and critical points within this model.

Main Methods:

  • Utilized the Ginzburg-Landau formalism.
  • Employed the mean-field approximation.
  • Performed analytical derivations.

Main Results:

  • Demonstrated a rich phase diagram for 1
  • Identified critical points, critical endpoints, and a novel tricritical point with unique supercritical behavior.
  • Microscopically explained discontinuous transitions arising from interaction-entropy competition or hidden state bistability.

Conclusions:

  • The q-state Potts model with hidden states presents complex phase behavior.
  • The identified novel supercritical behavior at the tricritical point expands understanding of phase transitions.
  • The study clarifies the microscopic origins of different transition types in spin systems.