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

2018/08/16 by Daniel Berkowitz, Berkowitz, Daniel · 1 citation
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #hep-th

paper · pdf · doi:10.48550/arxiv.1808.05862

4 pages

arxiv created 2018/08/16 · arxiv updated 2018/08/20

Abstract

We formulate the conformal mapping between R³ and S³, 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.

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