Conformal invariance and the Ising model on a 3 sphere in connection with the Quantum Elemental Method

TL;DR

This paper develops a conformal mapping between three-dimensional space and a sphere to analyze the critical 3D Ising model, calculating magnetization moments and Binder cumulant to compare with Quantum Elemental Method predictions.

Contribution

It introduces a conformal mapping approach for the 3D Ising model on a sphere and computes key statistical moments using Monte Carlo integration.

Findings

Calculated second and fourth moments of magnetization density.

Determined the 4th Binder cumulant for the 3D Ising model on a sphere.

Provides data for comparison with Quantum Elemental Method predictions.

Abstract

We formulate the conformal mapping between $R^3$ and $S^3$, the 3 sphere. This mapping is applied to the critical Ising model. From this mapping, we calculate the second and fourth moments of the magnetization density, and using those quantities calculate the 4th Binder cumulant. Our calculations for the critical 3D Ising Model on a 3 sphere are done using Mathematica's Monte Carlo Integration feature. The main motivation for performing this calculation is so we can later compare it to what the Quantum Elemental Method predicts.