Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The Ising model is a fundamental model in statistical mechanics used to study magnetism and phase transitions.
• Understanding phase diagrams and critical phenomena is crucial for predicting material properties.
• The triangular lattice presents unique geometric frustration effects relevant to magnetic ordering.

Purpose of the Study:

• To determine the phase diagram of the Ising model on a triangular lattice with nearest-neighbor (K(nn)) and next-nearest-neighbor (K(nnn)) couplings, and an external magnetic field (H).
• To characterize the nature of critical manifolds and phase transitions within this model.
• To explore both ferromagnetic and antiferromagnetic regimes, with a focus on the latter.

Main Methods:

• Finite-size scaling analysis of numerical results.
• Transfer matrix calculations.
• Monte Carlo simulations.

Main Results:

• A critical phase was identified for the antiferromagnetic case (K(nn) < 0) and zero magnetic field (H=0), potentially spanning the entire range of K(nn).
• A plane of phase transitions was located for K(nn) < 0 and non-zero H, featuring a line of tricritical three-state Potts transitions.
• In the limit of H approaching infinity, this line converges to a tricritical hard hexagon model with an attractive K(nnn) potential.

Conclusions:

• The study successfully maps the complex phase diagram of the Ising model on a triangular lattice under various conditions.
• The identified tricritical lines and their convergence to known models provide significant insights into critical phenomena.
• The research confirms the intricate interplay between lattice geometry, competing interactions, and external fields in magnetic systems.