Derivation of field theory for the classical dimer model using bosonization.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• The classical dimer model is a fundamental system in statistical mechanics.
• Existing height theory for the dimer model lacks precise field theory connections and coefficient determination.
• Bosonization techniques offer a powerful tool for mapping fermionic systems to bosonic field theories.

Purpose of the Study:

• To derive a field theory for the two-dimensional classical dimer model.
• To connect and validate results with the established height theory.
• To investigate the inclusion of interactions and analyze phase transitions.

Main Methods:

• Application of bosonization to Lieb's fermionic transfer-matrix solution.
• Constructive derivation of the effective field theory.
• Renormalization-group analysis for interacting dimer models.
• Perturbative treatment of interactions.

Main Results:

• A field theory for the classical dimer model consistent with height theory was derived.
• Specific coefficients in the effective theory and microscopic-observable relationships were determined.
• The phase boundary shape near the noninteracting point was calculated for interacting models.
• Agreement with Monte Carlo simulation results was achieved.

Conclusions:

• The bosonization approach provides a rigorous foundation for the field theory of the dimer model.
• This work clarifies the relationship between microscopic models and their continuum field theory descriptions.
• The methods are applicable to studying phase transitions in related interacting systems.