Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

TL;DR

This paper introduces a method using CTMRG to generate representative spin configuration snapshots in finite regions of infinite 2D classical lattice models, enabling detailed local analysis.

Contribution

It presents a novel approach to obtain local spin configurations in 2D classical models using CTMRG, bridging a gap in simulation techniques.

Findings

Enables stochastic fixing of spins based on conditional probabilities.

Provides a way to visualize typical configurations in infinite 2D models.

Utilizes the matrix product structure of CTMRG for efficient sampling.

Abstract

We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by each according to the conditional probability with respect to its environment.