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q-state Potts model from the nonperturbative renormalization group.

Carlos A Sánchez-Villalobos1,2, Bertrand Delamotte1, Nicolás Wschebor2

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Physical Review. E
|January 20, 2024
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This summary is machine-generated.

The q-state Potts model

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The q-state Potts model is a fundamental model in statistical mechanics.
  • Understanding phase transitions is crucial in condensed matter physics.

Purpose of the Study:

  • To determine the phase transition order for the q-state Potts model across various dimensions.
  • To identify the critical curve q_c(d) separating first and second-order transitions.

Main Methods:

  • Utilizing the nonperturbative renormalization group (NRPG) at leading order.
  • Employing derivative expansion, specifically the Local Potential Approximation (LPA and LPA').
  • Performing double expansion for small ε (4-d) and δ (q-2).

Main Results:

  • Derived the critical curve q_c(d) = 2 + aε² with a ≈ 0.1 for small ε.
  • Calculated q_c(d=3) = 2.11(7) by integrating NRPG flow equations.
  • Confirmed first-order phase transition for the three-state Potts model in d=3.

Conclusions:

  • The study provides a detailed phase diagram for the q-state Potts model.
  • Results confirm the first-order nature of the phase transition for the three-state Potts model in three dimensions.