Tensor Renormalization Group: Local Magnetizations, Correlation Functions, and Phase Diagrams of Systems with Quenched Randomness

TL;DR

This paper extends the tensor renormalization-group method to systems with quenched randomness, enabling accurate calculation of phase diagrams, local magnetizations, and correlation functions, exemplified by the bond-diluted Ising model.

Contribution

The study introduces a tensor renormalization-group approach for quenched disordered systems, providing a systematic way to compute phase diagrams and thermodynamic properties.

Findings

Accurate phase diagram for the bond-diluted Ising model.

Method effectively captures long-distance correlation behavior.

Results valid down to the percolation threshold at zero temperature.

Abstract

The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched randomness, is extended in this study to systems with quenched randomness. Local magnetizations and correlation functions as a function of spin separation are calculated as tensor products subject to renormalization-group transformation. Phase diagrams are extracted from the long-distance behavior of the correlation functions. The approach is illustrated with the quenched bond-diluted Ising model on the triangular lattice. An accurate phase diagram is obtained in temperature and bond-dilution probability, for the entire temperature range down to the percolation threshold at zero temperature.