Two-dimensional XXZ-Ising model with quartic interactions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Many-Body Systems

Background:

• Investigating complex spin models is crucial for understanding emergent phenomena in materials.
• The XXZ-Ising model provides a framework for studying magnetic properties and phase transitions.
• Quartic interactions introduce novel complexities beyond standard pairwise couplings.

Purpose of the Study:

• To analyze a two-dimensional XXZ-Ising spin-1/2 model incorporating quartic interactions.
• To construct the zero-temperature phase diagram and identify all possible spin configurations.
• To explore exact solvability conditions, specifically the free fermion condition (FFC) and symmetrical eight-vertex condition (SEVC).

Main Methods:

• Development of a two-dimensional lattice model with edge-sharing unitary cells.
• Construction of the phase diagram at zero temperature.
• Mapping the model to a zero-field eight-vertex model to analyze exact solvability.
• Investigation of conditions for the free fermion condition and symmetrical eight-vertex condition.

Main Results:

• The proposed model does not satisfy the free fermion condition, except in a trivial case.
• A region where the model can be solved approximately was identified.
• The symmetrical eight-vertex condition is consistently satisfied for the model.
• Critical conditions and relevant critical points were explored and discussed.

Conclusions:

• The study provides a comprehensive analysis of the 2D XXZ-Ising spin-1/2 model with quartic interactions.
• The findings highlight the model's behavior under specific solvability conditions (SEVC) and its limitations (FFC).
• This research contributes to the understanding of phase diagrams and critical phenomena in complex magnetic systems.