Supplementary material to 'Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models'

I. GENERAL INFORMATION 1. Title<br> Dataset of "Degeneracy and Scaling Properties of Self-Dual Fracton Spin Models" 2. Author Information<br> <br> Giovanni Canossa [1,2], Lode Pollet [1,2,3], Miguel A. Martin-Delgado [4], Hao Song [5], and Ke Liu [1,2]<br> 1. Arnold Sommerfeld Center for Theoretical Physics, University of Munich<br> 2. Munich Center for Quantum Science and Technology (MCQST)<br> 3. Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University<br> 4. Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain<br> 5. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China Links to publications that cite or use the data:<br> TBA II. Files 1. Convention Datas from the multicanonical MC simulations are stored in "Tetra-Ising" and "Fractal-Ising" folders. Lattice size: Each subfolder is named "L=value" where value denotes the linear system size. Multicanonical weights: Files "g_init_T=value.data" contains the set of log(weights) at a given temperature and lattice size, derived from the iterative weight-learning procedure. Datas: HDF5 files "name.out.h5" contain the results of the multicanonical MC simulation at a given lattice size. <br> III. Data in HDF5 file 1. Convention The results obtained at each temperature point is stored in a separate subdirectory of the .out.h5 file. Each of these subdirectories contains: Energy_Hist: normalized energy histograms obtained from the multicanonical MC simulation (unweighted) Energy_Hist_rw: normalized reweighted energy histograms. For each bin, Energy_Hist_rw[i] = Energy_Hist[i] * e**g[i] / norm, where norm = sum( Energy_Hist[i] * e**g[i] ). c: 1/norm. Gives an estimate of the ratio Z_muca/Z_ca. g: vector containing the weights used for the multicanonical MC simulation at that specific temperature. These are derived from reweighting the weights in "g_init_T=value.data" file. Energy, Energy_Susc, Energy_Kurt Q_x, Q_x_Susc, Q_x_Kurt: canonical expectation value of each relevant observables, along with their susceptibilities and Kurtosis, obtained by reweighting each measurement taken during the simulation by the appropriate weight. (NB: Energy and Q_x need to be multiplied by C in order to give the correct canonical expectation value.) <br> 2. Relevance These data reproduce Figs. 5 &amp; 6 in the manuscript. <br> III. Finite size scaling 1. Convention All estimated transition temperatures with their respective uncertainties are stored in "fitting_Tetra" and "fitting_Fractal" folders in the fittemps.txt file. 2. Relevance These data reproduce Figs. 3 &amp; 4 in the manuscript.<br>