Quantum phase transitions in the Ising model in a spatially modulated field

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Quantum magnetism

Background:

• The transverse field Ising model is a fundamental model in statistical mechanics.
• Investigating phase transitions under competing fields is crucial for understanding complex magnetic systems.

Purpose of the Study:

• To numerically study phase transitions in the transverse field Ising model with a competing spatially modulated longitudinal field.
• To analyze the critical exponents and universality class of the observed phase transitions.

Main Methods:

• Numerical simulations were employed to study the model.
• Phase transitions were identified by the vanishing of the mass gap (Delta).
• Finite size scaling analysis was performed to characterize the transitions.

Main Results:

• Continuous phase transitions were observed across the studied phase diagram.
• The critical exponents align with the universality class of the two-dimensional Ising model.
• A unique scaling behavior was found for the longitudinal field, mirroring the transverse field.
• Phase boundaries were determined for different longitudinal field wavelengths, showing dependence near a multiphase point.

Conclusions:

• The model exhibits continuous phase transitions belonging to the 2D Ising universality class.
• The competing longitudinal field introduces unique scaling properties.
• The findings contribute to the understanding of phase transitions in complex magnetic systems.