Tensor-network study of Ising model on infinite hyperbolic dodecahedral lattice

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The classical Ising model is a fundamental tool for understanding magnetism and phase transitions.
• Studying models on complex lattices, like hyperbolic ones, presents significant computational challenges.
• Existing methods often struggle with infinite-dimensional or non-Euclidean structures.

Purpose of the Study:

• To develop and apply a novel tensor-network algorithm for the Ising model on a 3D hyperbolic dodecahedral lattice.
• To investigate the nature of phase transitions in this complex lattice geometry.
• To determine critical exponents and compare them with theoretical predictions.

Main Methods:

• Reformulation of the 2D corner transfer matrix renormalization group (CTMRG) algorithm into 3D.
• Generalization of the CTMRG algorithm to an infinite-dimensional hyperbolic lattice with dodecahedral cells.
• Analysis of physical quantities including spontaneous magnetization, von Neumann entropy, and correlation length.

Main Results:

• A continuous noncritical phase transition was identified on the dodecahedral lattice.
• The estimated phase transition temperature was determined.
• Magnetic critical exponents (β=0.4999, δ=3.007) were calculated, confirming the mean-field universality class.

Conclusions:

• The developed tensor-network algorithm is effective for studying the Ising model on hyperbolic lattices.
• The findings align with Monte Carlo and high-temperature series expansion predictions.
• The algorithm's applicability extends to arbitrary multistate spin models.