Tensor-network study of Ising model on infinite hyperbolic dodecahedral lattice.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 42316677.
- Also identified by DOI 10.1103/nzyw-2zxt.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group (CTMRG) algorithm from 2D to 3D to reproduce the known results on the cubic lattice. We subsequently generalize the CTMRG to a hyperbolic lattice with dodecahedral cells, which is an infinite-dimensional lattice. We analyze the spontaneous magnetization, von Neumann entropy, and correlation length to find a continuous noncritical phase transition on the dodecahedral lattice. We estimate the phase-transition temperature and find the magnetic critical exponents β=0.4999 and δ=3.007, which confirm the mean-field universality class, in accord with predictions from Monte Carlo and high-temperature series expansions. The algorithm can be applied to arbitrary multistate spin models.