Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach
This is an incremental application of deep learning to condensed matter physics, potentially aiding researchers in analyzing thermodynamic systems.
The study tackled computing critical exponents in the 3D Ising model using a deep learning approach, achieving a test accuracy of 0.6875 on spin state classifications but noting that more work is needed to quantify feasibility for exponent computation.
In this study, we computed three critical exponents ($α, β, γ$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised Deep Learning (DL) approach (3D Convolutional Neural Network or CNN) to train a neural network on specific conformations of spin states. We find one can effectively reduce the information in thermodynamic ensemble-averaged quantities vs. reduced temperature t (magnetization per spin $<m>(t)$, specific heat per spin $<c>(t)$, magnetic susceptibility per spin $<χ>(t)$) to \textit{six} latent classes. We also demonstrate our CNN on a subset of L=20 conformations and achieve a train/test accuracy of 0.92 and 0.6875, respectively. However, more work remains to be done to quantify the feasibility of computing critical exponents from the output class labels (binned $m, c, χ$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general.