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We derived three-loop renormalization group equations for polymerized membranes. Our results for the field anomalous dimension (η) closely match nonperturbative methods and theoretical values.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Polymer Physics

Background:

  • Polymerized membranes exhibit complex phases, including a flat phase.
  • Previous studies computed renormalization group equations at one- and two-loop orders.
  • Understanding membrane behavior requires higher-order theoretical analysis.

Purpose of the Study:

  • To derive three-loop order renormalization group equations for the flat phase of polymerized membranes.
  • To analyze the fixed points of these equations.
  • To compute the field anomalous dimension (η) at three-loop order.

Main Methods:

  • Utilized the modified minimal subtraction scheme.
  • Extended previous one- and two-loop order calculations.
  • Analyzed fixed points and computed the anomalous dimension.

Main Results:

  • Derived the three-loop order renormalization group equations.
  • Computed the field anomalous dimension (η) at three-loop order.
  • Obtained η=0.8872 at the stable fixed point in D=2, showing proximity to nonperturbative results.

Conclusions:

  • The three-loop calculations provide a more accurate description of polymerized membrane behavior.
  • Results are consistent with nonperturbative techniques and known theoretical values.
  • The computed anomalous dimension is within the range of accepted numerical values.