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Classifying Potts critical lines.

Gesualdo Delfino1, Elena Tartaglia1

  • 1SISSA-Via Bonomea 265, 34136 Trieste, Italy and INFN sezione di Trieste, 34100 Trieste, Italy.

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We precisely mapped renormalization group fixed points using scale invariant scattering theory. This reveals new critical lines for the q-state Potts model, extending the known range for antiferromagnetic transitions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Renormalization group (RG) fixed points are crucial for understanding critical phenomena in statistical physics.
  • The q-state Potts model is a fundamental model in statistical mechanics, exhibiting diverse phase transitions.
  • Permutational symmetry (S_{q}) plays a key role in classifying the behavior of the q-state Potts model.

Purpose of the Study:

  • To exactly determine the lines of RG fixed points invariant under S_{q} symmetry in two dimensions.
  • To identify which of these RG fixed points correspond to known ferromagnetic and antiferromagnetic critical lines of the q-state Potts model.
  • To explore the existence of new, previously undiscovered critical lines.

Main Methods:

  • Employing scale invariant scattering theory to analyze RG fixed points.
  • Investigating the behavior of these fixed points under S_{q} symmetry.
  • Calculating the maximal value of q for which S_{q}-invariant fixed points exist.

Main Results:

  • One RG fixed point solution accurately describes the ferromagnetic and square lattice antiferromagnetic critical lines of the q-state Potts model.
  • Other determined RG fixed point solutions indicate the presence of new critical lines.
  • A S_{q}-invariant fixed point was found to exist up to q=(7+sqrt[17])/2, exceeding the previously assumed maximum of 4.

Conclusions:

  • The study provides an exact determination of S_{q}-invariant RG fixed points in 2D.
  • New critical lines for the q-state Potts model are identified, expanding our understanding of its phase diagram.
  • The findings suggest the possibility of a second-order antiferromagnetic transition at q=5, challenging previous assumptions.