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The study on the q-state Potts model reveals second-order phase transitions for q≤4 and first-order for q>4. An improved upper bound for the critical temperature, T_{c}, was found to be 1/(θlnq).

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The q-state Potts model is a fundamental model in statistical mechanics.
  • Understanding phase transitions in lattice models is crucial for various physical systems.
  • The role of multi-site interactions, like four-site interactions, can significantly alter model behavior.

Purpose of the Study:

  • To investigate the phase transitions of the q-state Potts model with four-site interaction on a square lattice.
  • To determine the order of the phase transition based on the value of q.
  • To derive and improve bounds for the critical temperature (T_{c}) and explore its relationship with q.

Main Methods:

  • Theoretical analysis using the asymptotic behavior of lattice animals.
  • Low-temperature expansion to derive improved upper bounds for T_{c}.
  • Numerical confirmation using the Wang-Landau entropic sampling method.

Main Results:

  • The system exhibits a second-order phase transition for q≤4 and a first-order transition for q>4.
  • An upper bound for T_{c} was established as 1/lnq, with an improved bound of 1/(θlnq).
  • Numerical simulations for q=3, 4, and 5 confirmed theoretical predictions, with the q=4 model showing ambiguous finite-size pseudocritical behavior.

Conclusions:

  • The derived expression T_{c}=1/(θlnq) provides a strong estimate for the critical temperature.
  • The findings offer insights into estimating finite correlation lengths in first-order transition systems.
  • The results are generalizable to other lattice structures and interactions.