1. ABOUT THE DATASET -------------------- Title: Supporting data for "Conformal scalar field theory from Ising tricriticality on the fuzzy sphere". Creator(s): Joseph Taylor[1], Cristian Voinea[1], Zlatko Papic[1], Ruihua Fan[2]. Organisation(s): 1. School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom. 2. Department of Physics, University of California, Berkeley, CA 94720, USA Rights-holder(s): Copyright 2026 University of Leeds Publication Year: 2026 Description: This dataset provides numerical results for a realisation of a free scalar conformal field theory (CFT) in 2+1 dimensions. It includes conformal spectra, conformal perturbation coefficients, finite-size scaling data, free-energy calculations, and algebraic structures of the free-boson operator content. The files contain energy levels, operator dimensions, order parameter data and structural constants derived from numerical computations. Cite as: Taylor, Joseph, Voinea, Cristian, Papic, Zlatko and Fan, Ruihua (2026) Supporting data for "Conformal scalar field theory from Ising tricriticality on the fuzzy sphere". University of Leeds. [Dataset] https://doi.org/10.5518/1789 Related publication: Joseph Taylor, Cristian Voinea, Zlatko Papic, Ruihua Fan. Conformal scalar field theory from Ising tricriticality on the fuzzy sphere. Physical Review Letters (2025) (Accepted). https://doi.org/10.1103/cj3l-cf58 Contact: Corresponding author: Joseph Taylor Email: pyjpct@leeds.ac.uk Affiliation: School of Physics and Astronomy, University of Leeds, UK 2. TERMS OF USE --------------- Copyright 2026 University of Leeds. Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/ 3. PROJECT AND FUNDING INFORMATION ---------------------------------- Title: Conformal scalar field theory from Ising tricriticality on the fuzzy sphere Funding organisation: EPSRC Grant no.: EP/Z533634/1, UKRI1337 Funding organisation: Leverhulme Trust Grant no.: RL-2019-015 Funding organisation: Gordon and Betty Moore Foundation Grant no.: GBMF8688 Funding organisation: Kavli Institute for Theoretical Physics (KITP) Grant no.: NSF PHY-2309135 Acknowledgements: The Erwin Schrödinger International Institute for Mathematics and Physics. 4. CONTENTS ----------- All data are plain-text columns containing numerical arrays suitable for plotting. The files can be read using any standard data analysis software (Python, Julia, MATLAB, etc.). Each numbered folder corresponds to a figure in the publication: | Folder | Content summary |--------|--------------------------------------------------------------------------------------------------------------------------------------------------- | Fig1/ | Folders Fig1b/ and Fig1c/ containing data used to generate the two spectra subplots Fig. 1b and Fig. 1c respectively | | The .txt file names are labelled as {system size}_spectrum_{descriptor}_Fig{figure number}{panel label}.txt. | | The columnns of each .txt file within a folder represent | Scaling dimension | Raw Energy | L^2 eigenvalue | P sector | Z sector |. |--------|--------------------------------------------------------------------------------------------------------------------------------------------------- | Fig2/ | Folders Fig2a/, Fig2b/, Fig2c/ and Fig2d/ containing raw data used to generate the subplots of Fig. 2. | | The data for each subplot is in its aptly named folder. | | | | Fig2a/ and Fig2c/ : | | - The .txt file names are labelled as {system size}_Magnetisation_Fig{figure number}{panel label}.txt. | | - The first column of each .txt file is the transition parameter, \lambda, along the x-axis. | | - The second column is the unscaled . To recreate the plot, a system size rescaling | | that is detailed in our manuscript must be applied to acquire the correct y-coordinate values. | | | | Fig2b/ : | | - The .txt file names are labelled as {system size}_Magnetisation_Fig{figure number}{panel label}.txt. | | - The first column of each .txt file is the transition paramater, h, along the x-axis. | | - The second column is the unscaled . To recreate the plot, a system size rescaling | | that is detailed in our manuscript must be applied to acquire the correct y-coordinate values. | | | | Fig2d/ : | | - The .txt file names are labelled as {system size}_GSE_Fig{figure number}{panel label}_{location}.txt. | | - The first column of each .txt file is the unscaled transition paramater, \lambda. | | - The second column is the unscaled ground state energy density, \epsilon. | | - This raw data generates Fig. S9 in the supplementary material of our manuscript. | | - To generate Fig. 2d, one must apply the scaling ansatz detailed in the supplementary material | | of our manuscript and take a discrete derivative. | | - Data for the main plot of Fig. 2d are labelled _main.txt and _inset.txt for the inset. |--------|--------------------------------------------------------------------------------------------------------------------------------------------------- | Fig3/ | Contains all the raw data used to generate Fig. 3a and Fig. 3b. | | The .txt file names are labelled as {system size}_free_tower.txt. | | The nth line of a .txt file is the overlap where Nz is crucially unscaled and |n> is the nth L=0 state. | | To acquire the values for p(n)= as detailed in the manuscript, we do p(n) = * N^(-0.75) for system size N. | | We then plot p(n)/sqrt(n!) against n. For the theoretically expected curve, one extrapolates as in Fig. 3b the n=1 values across system sizes | | and the y-axis interception is the value of a_1 used to acquire the theoretically expected straight line. |--------|--------------------------------------------------------------------------------------------------------------------------------------------------- | Fig4/ | Contains all the raw data used to generate Fig. 3a and Fig. 3b. | | | | Fig4a/ : | | - The .txt file names are labelled as {system size}_spectrum_{descriptor}_Fig{figure number}{panel label}.txt. | | - The data contained here is the same as the folder Fig1b/. | | - Conformal perturbation theory, detailed in the supplementary material, was appled to these spectra to | | calculate the coefficients of the \phi^2, \phi^4 and \phi^6 operators at the tricritical point. | | | | Fig4b/ : | | - The .txt file names are labelled as {system size}_cnf_coeff_{operator}_Fig{figure number}{panel label}.txt. | | - The columns of each .txt file represent | h | \lambda | coefficient | | | - Each row gives a h and \lambda value such that the spectrum at that point in the phase diagram has a | | conformal operator perturbation coefficient of the last value in the row. | | - This data was acquired by attaining the spectra at each point plotted in Fig. 4b. This data is available upon request. | | Conformal perturbation theory was applied to these spectra to acquire the data in folder Fig4b/. |--------|--------------------------------------------------------------------------------------------------------------------------------------------------- File formats: txt 5. METHODS ---------- Computational portions of this research have made use of DiagHam however all the data was generated using the FuzzifiED.jl library (Julia 1.10) to be cited as FuzzifiED : Julia package for numerics on the fuzzy sphere, Zheng Zhou, arXiv:2503.00100. Computation was carried out on ARC4 and AIRE, part of the High-Performance Computing facilities at the University of Leeds. All relevant source code is available from the corresponding author upon reasonable request.