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arXiv · 2608.17006

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

Kai Svenson·George T. Fleming·Richard C. Brower·Nobuyuki Matsumoto·Rohan Misra
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Abstract

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $\beta_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $\beta_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

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Kai Svenson, George T. Fleming, Richard C. Brower, Nobuyuki Matsumoto, Rohan Misra. 2026-08-17. Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow. https://arxiv.org/abs/2608.17006

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