Wrinkling transition in quenched disordered membranes at two loops

Area of Science:

• Condensed Matter Physics
• Polymer Physics
• Statistical Mechanics

Background:

• Polymerized membranes exhibit complex phases influenced by quenched disorder.
• Understanding the flat phase and its transitions is crucial for membrane physics.
• Previous studies explored these phenomena using one-loop and nonperturbative renormalization group methods.

Purpose of the Study:

• To investigate the flat phase of quenched disordered polymerized membranes.
• To generalize existing one-loop computations to a two-loop level.
• To confirm the existence and properties of the wrinkling transition.

Main Methods:

• Two-loop, weak-coupling computation near the upper critical dimension (D_uc=4).
• Generalization of prior one-loop calculations.
• Comparison with nonperturbative renormalization group results.

Main Results:

• Confirmation of the finite-temperature, finite-disorder wrinkling transition.
• Identification of ambiguities in the two-loop computation.
• Indication that a three-loop approach may be necessary for precise characterization.

Conclusions:

• The wrinkling transition in disordered polymerized membranes is robust.
• The two-loop computation provides valuable insights but has limitations.
• Further theoretical development is required to fully understand the novel fixed point of the wrinkling transition.