Dense loops, supersymmetry, and Goldstone phases in two dimensions

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• Two-dimensional loop models exhibit connections to O(N) models.
• A low-temperature dense-loops phase can display a Goldstone broken-symmetry phase for N<2.

Purpose of the Study:

• To investigate the conditions under which a Goldstone broken-symmetry phase emerges in two-dimensional loop models.
• To differentiate this phase from previously studied noncrossing dense loop models.

Main Methods:

• Theoretical analysis relating loop models to O(N) and supergroup models.
• Numerical simulations to support theoretical arguments.
• Examination of an exactly solved lattice model.

Main Results:

• The Goldstone broken-symmetry phase is demonstrated to be generic for -2
• This phase is shown to be distinct from the noncrossing dense loop model.
• Numerical and exact lattice model results corroborate the theoretical findings.

Conclusions:

• The presence of loop crossings significantly influences the low-temperature behavior of two-dimensional loop models.
• A new universality class for dense loop models is identified for the parameter range -2