Tensor network simulation for the frustrated J_{1}-J_{2} Ising model on the square lattice

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Information

Background:

• The J1-J2 Ising model on a square lattice exhibits complex magnetic ordering.
• The phase diagram, particularly the stripe transition for |J2/J1| > 1/2, remains a subject of debate.
• Previous studies proposed a first-order phase transition in a specific regime.

Purpose of the Study:

• To accurately map the phase diagram of the frustrated J1-J2 Ising model.
• To resolve controversies regarding the stripe transition and its order.
• To investigate the critical properties and universality classes involved.

Main Methods:

• Extensive tensor network calculations were employed.
• Simulations focused on the regime |J2/J1| > 1/2 with J2>0 and J1<0.
• Analysis of critical properties and central charge was performed.

Main Results:

• The study suggests that the first-order phase transition region, if present, is smaller than previously estimated.
• Evidence points towards a continuous evolution of the model.
• The tricritical Ising universality class (central charge c=0.7) is identified as g approaches approximately 0.54.

Conclusions:

• The J1-J2 Ising model transitions continuously from decoupled Ising models to the tricritical Ising universality class.
• The findings refine the understanding of the model's phase diagram and critical behavior.
• This work provides crucial insights into frustrated magnetic systems.