Ising transition driven by frustration in a 2D classical model with continuous symmetry

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Quantum magnetism

Background:

• The classical antiferromagnetic Heisenberg model on a square lattice exhibits complex behavior influenced by nearest-neighbor (J1) and next-nearest-neighbor (J2) exchange couplings.
• Understanding the thermal properties and phase transitions in such models is crucial for developing new magnetic materials and understanding quantum phenomena.

Purpose of the Study:

• To investigate the thermal properties of the classical antiferromagnetic Heisenberg model with both J1 and J2 couplings on a square lattice.
• To identify and characterize any finite-temperature phase transitions induced by thermal fluctuations.
• To determine the universality class of the observed phase transition.

Main Methods:

• Extensive Monte Carlo simulations were employed to study the thermal properties.
• Analysis focused on the emergence of effective Z2 symmetry for specific coupling ratios (J2/J1 > 1/2).
• Numerical evidence was gathered to classify the phase transition within established universality classes.

Main Results:

• For J2/J1 > 1/2, thermal fluctuations induce an effective Z2 symmetry.
• A finite-temperature phase transition was observed under these conditions.
• Strong numerical evidence indicates the transition belongs to the 2D Ising universality class.
• The critical temperature T(c) approaches zero with an infinite slope as J2/J1 approaches 1/2.

Conclusions:

• The classical antiferromagnetic Heisenberg model with competing J1 and J2 couplings exhibits a finite-temperature phase transition.
• This transition is driven by thermal fluctuations and falls within the 2D Ising universality class.
• The model's behavior near J2/J1 = 1/2 suggests a critical endpoint with unique scaling properties.