Multi-Spin Coding of the Monte Carlo Simulation of the Three-State Random Potts Model and the Block-Spin Transformation

TL;DR

This paper presents a multi-spin coding approach for Monte Carlo simulations of the three-state Potts model, including ferromagnetic, antiferromagnetic, and mixed couplings, and applies it to block-spin transformations.

Contribution

It introduces a multi-spin coding technique for the three-state Potts model and demonstrates its application to block-spin transformations with different coupling types.

Findings

Multi-spin coding effectively simulates the three-state Potts model.

Block-spin transformation is simplified for ferromagnetic models.

Antiferromagnetic models transform into six-fold symmetric spins.

Abstract

The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are treated. The multi-spin coding technique is also applied to the block-spin transformation. The block-spin transformation of the F Potts model is simply realized by the majority rule, whereas the AF three-state Potts model is transformed to the block spin having a six-fold symmetry.