Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach

• URL: http://arxiv.org/abs/2411.02604v1
• Date: Mon, 04 Nov 2024 20:57:24 GMT
• Title: Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach
• Authors: Timothy A. Burt,
• Abstract summary: We perform a supervised Deep Learning approach to train a neural network on specific conformations of spin states. We achieve a train/test accuracy of 0.92 and 0.6875, respectively. More work remains to be done to quantify the feasibility of computing critical exponents from this approach.
• Score: 1.6317061277457001
• License:
• Abstract: In this study, we computed three critical exponents ($\alpha, \beta, \gamma$) 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 $<\chi>(t)$) 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 $m, c, \chi$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general.

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