Mean-field universality class induced by weak hyperbolic curvatures.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Geometric Frustration

Background:

• The Ising model is a fundamental model in statistical mechanics for studying magnetism and phase transitions.
• Investigating phase transitions on curved surfaces introduces geometric frustration, impacting critical phenomena.
• Understanding how negative Gaussian curvature affects magnetic order is crucial for materials science.

Purpose of the Study:

• To explore the order-disorder phase transition of the ferromagnetic Ising model on 2D lattices with negative Gaussian curvature.
• To analyze the influence of lattice geometry and exceptional sites on spontaneous magnetization and specific heat.
• To examine the relationship between entanglement entropy and lattice curvature at the transition temperature.

Main Methods:

• Utilized the corner transfer matrix renormalization group (CTMRG) method for calculations.
• Investigated a series of 2D triangular lattices with engineered exceptional sites.
• Analyzed spontaneous magnetization, specific heat, and entanglement entropy.

Main Results:

• Observed mean-field-like phase transitions for all finite values of the parameter n.
• Confirmed that entanglement entropy at the transition temperature scales linearly with (c/6)ln n.
• Demonstrated that the typical length scale n is proportional to the curvature radius.

Conclusions:

• Negative Gaussian curvature on 2D lattices leads to mean-field-like phase transitions in the ferromagnetic Ising model.
• Entanglement entropy provides a quantitative measure of the influence of curvature on critical behavior.
• The findings support the connection between geometric properties of lattices and their thermodynamic critical phenomena.