DOI: 10.5061/dryad.v15dv427n
title: Data from: Emergent electrostatics in planar XY spin models: The bridge connecting topological order with broken U(1) symmetry

description: Topological phases have been a central focus of condensed-matter physics
 for over 50 years.  Along with many experimental applications,
 they have provided much intellectual interest due to their
 characterization via some form of topological ordering, as opposed to the
 symmetry-breaking ordering of conventional continuous phase transitions.
  This distinction is most subtle in the case of the
 Berezinskii—Kosterlitz—Thouless (BKT) transition as its experimental
 realizations appear to break U(1) symmetry at low temperature.
  It also presents two further paradoxes: i) its prototypical
 short-range interacting planar XY spin model behaves as an emergent
 long-range interacting electrolyte; ii) its topological ordering is not
 accompanied by a topological nonergodicity within the BKT picture.
  This data deposit supports a review paper that addresses these
 three interconnected questions.  In particular, it provides the
 simulation data that supports the concept of topological nonergodicity
 throughout the low-temperature phase.  Simulation data that
 supports the concept of broken U(1) symmetry (at low temperature) is
 reproduced from another research article.  This data was stored
 in the University of Bristol data repository, data.bris, with DOI
 10.5523/bris.3ov1rl6xtshwv2iuixrbs6f39q.  Simulation data used to
 demonstrate low-temperature broken symmetry in the two-dimensional Ising
 model is also provided in the present data deposit.
description: # Emergent electrostatics in planar XY spin models: The bridge connecting
 topological order with broken U(1) symmetry Dataset DOI:
 [10.5061/dryad.v15dv427n](10.5061/dryad.v15dv427n) ## Description of the
 data and file structure This data deposit contains simulation data that
 supports the paper (published by Michael F. Faulkner) entitled: *Emergent
 electrostatics in planar XY spin models: the bridge connecting topological
 order with broken U(1) symmetry*.  We refer to this paper as *Emergent
 electrostatics* below. The majority of the simulation data contained in
 the present deposit is that used to support the concept of topological
 nonergodicity throughout the low-temperature phase of planar XY spin
 models. Simulation data that supports the concept of broken *U*(1)
 symmetry (at low temperature) is reproduced (within the above paper) from
 another research article.  This data was stored in the University of
 Bristol data repository, data.bris, with DOI
 10.5523/bris.3ov1rl6xtshwv2iuixrbs6f39q. Simulation data used to
 demonstrate low-temperature broken symmetry in the two-dimensional Ising
 model is also provided in the present data deposit. ### Files and
 variables #### File: emergent\_electrostatics\_dryad\_upload.zip
 **Description:**  This zip file is the sole component of the data deposit.
  It contains three directories (emergent_electrostatics_ising_figs,
 global_top_trace_plots and top_susc_figs) which contain the .tsv and .npy
 files listed in the file inventories below.  To use the data contained in
 these files, follow the instructions outlined in the
 section **Code/software** found at the end of this README file. Each .npy
 file contains a Monte Carlo sample of some quantity (as a numpy array).
  Each .tsv file contains summary statistics generated using Monte Carlo
 samples.  The column headings (in each .tsv file) denote the quantities in
 the corresponding columns.  The quantities are those presented in figures
 14—17 of *Emergent electrostatics*.  With the exception of chi*_*ratio,
 each quantity is named as defined for those figures.  Each chi*_*ratio in
 the files entitled topological_susceptibility_ratio_*.*tsv is the
 expression defined inside the square root of equation (68) of Emergent
 electrostatics.  The other instances of chi_*ratio are defined analogously
 (with respect to the corresponding quantity) as described in figure 16 of
 Emergent electrostatics.  For absolute clarity, please refer to the Python
 scripts (described in the section **Code/software** found at the end of
 this README file) that make the aforementioned figures.  All units of
 measurement are dimensionless. The naming conventions of the files are as
 follows:  Each file of the form
 LxL_ising_model_temperature_0p_reduced_magnetic_density_sample_ALGORITHM_algorithm.npy contains the Monte Carlo sample of the magnetic density (without the equilibration steps, hence "reduced") of the Ising model on an LxL lattice generated using the ALGORITHM algorithm at temperature index p in the corresponding configuration file (for more details on configuration files, see the instructions in the section **Code/software** found at the end of this README file). Each file of the form OBSERVABLE_MODEL&ALGORITHM_LxL_sites_n_obs_temp_eq_TEMP_run_m.npy contains the Monte Carlo sample (of size n) of OBSERVABLE (without the equilibration steps) of the MODEL model on an LxL lattice generated (by independent run m) using the ALGORITHM algorithm at temperature TEMP. Each file of the form OBSERVABLE_vs_temperature_MODEL&ALGORITHM_LxL_sites_mxn_obs.tsv contains estimates of OBSERVABLE versus temperature of the MODEL model on an LxL lattice (estimated using m independent Monte Carlo samples of size n, each generated using the ALGORITHM algorithm). NB, the algorithm name is not given (beyond whether global moves are used) for the lattice electrolyte, as only the Metropolis algorithm is available for this model. **File inventories:** Inventory of all files contained in emergent_electrostatics_ising_figs: 16x16_ising_model_temperature_00_reduced_magnetic_density_sample_metropolis_algorithm.npy 16x16_ising_model_temperature_00_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 16x16_ising_model_temperature_01_reduced_magnetic_density_sample_metropolis_algorithm.npy 16x16_ising_model_temperature_01_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 16x16_ising_model_temperature_02_reduced_magnetic_density_sample_metropolis_algorithm.npy 16x16_ising_model_temperature_02_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 32x32_ising_model_temperature_00_reduced_magnetic_density_sample_metropolis_algorithm.npy 32x32_ising_model_temperature_00_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 32x32_ising_model_temperature_01_reduced_magnetic_density_sample_metropolis_algorithm.npy 32x32_ising_model_temperature_01_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 32x32_ising_model_temperature_02_reduced_magnetic_density_sample_metropolis_algorithm.npy 32x32_ising_model_temperature_02_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 4x4_ising_model_temperature_00_reduced_magnetic_density_sample_metropolis_algorithm.npy 4x4_ising_model_temperature_00_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 4x4_ising_model_temperature_01_reduced_magnetic_density_sample_metropolis_algorithm.npy 4x4_ising_model_temperature_01_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 4x4_ising_model_temperature_02_reduced_magnetic_density_sample_metropolis_algorithm.npy 4x4_ising_model_temperature_02_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 64x64_ising_model_temperature_00_reduced_magnetic_density_sample_metropolis_algorithm.npy 64x64_ising_model_temperature_00_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 64x64_ising_model_temperature_01_reduced_magnetic_density_sample_metropolis_algorithm.npy 64x64_ising_model_temperature_01_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 64x64_ising_model_temperature_02_reduced_magnetic_density_sample_metropolis_algorithm.npy 64x64_ising_model_temperature_02_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 8x8_ising_model_temperature_00_reduced_magnetic_density_sample_metropolis_algorithm.npy 8x8_ising_model_temperature_00_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 8x8_ising_model_temperature_01_reduced_magnetic_density_sample_metropolis_algorithm.npy 8x8_ising_model_temperature_01_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy 8x8_ising_model_temperature_02_reduced_magnetic_density_sample_metropolis_algorithm.npy 8x8_ising_model_temperature_02_reduced_magnetic_density_sample_swendsen_wang_algorithm.npy Inventory of all files contained in global_top_trace_plots: electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_0.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_1.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_10.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_11.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_12.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_13.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_14.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_15.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_16.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_17.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_18.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_19.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_2.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_20.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_21.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_22.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_23.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_24.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_25.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_26.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_27.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_28.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_29.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_3.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_30.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_31.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_32.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_33.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_34.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_35.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_36.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_37.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_38.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_39.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_4.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_40.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_41.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_42.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_43.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_44.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_45.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_46.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_47.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_5.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_6.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_7.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_8.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_0.9493_run_9.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_0.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_1.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_10.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_11.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_12.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_13.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_14.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_15.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_16.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_17.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_18.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_19.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_2.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_20.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_21.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_22.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_23.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_24.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_25.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_26.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_27.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_28.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_29.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_3.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_30.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_31.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_32.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_33.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_34.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_35.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_36.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_37.npy 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electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_45.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_46.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_47.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_5.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_6.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_7.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_8.npy electric_field_zero_mode_elementary_electrolyte_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.4989_run_9.npy file_list.txt 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xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_47.npy xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_5.npy xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_6.npy xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_7.npy xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_8.npy xy_twist_relaxation_field_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_10000_obs_temp_eq_1.5068_run_9.npy Inventory of all files contained in top_susc_figs: acceptance_rates_vs_temperature_elementary_electrolyte_sans_global_moves_128x128_sites_1536x1000000_obs.tsv acceptance_rates_vs_temperature_elementary_electrolyte_sans_global_moves_16x16_sites_1536x1000000_obs.tsv 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inverse_permittivity_vs_temperature_elementary_electrolyte_w_global_moves_8x8_sites_1536x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_128x128_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_16x16_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_32x32_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_4x4_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_64x64_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_8x8_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_128x128_sites_384x1000000_obs.tsv 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inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_4x4_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_8x8_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_128x128_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_16x16_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_32x32_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_4x4_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_64x64_sites_384x1000000_obs.tsv inverse_vacuum_permittivity_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_hxy_uniform_noise_metropolis_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_ratio_xy_uniform_noise_metropolis_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_sans_global_moves_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_hxy_uniform_noise_metropolis_w_global_moves_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_sans_global_moves_8x8_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_128x128_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_16x16_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_32x32_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_4x4_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_64x64_sites_384x1000000_obs.tsv josephson_susceptibility_vs_temperature_xy_uniform_noise_metropolis_w_global_moves_8x8_sites_384x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_128x128_sites_1536x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_16x16_sites_1536x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_32x32_sites_1536x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_4x4_sites_1536x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_64x64_sites_1536x1000000_obs.tsv topological_susceptibility_ratio_elementary_electrolyte_8x8_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_128x128_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_16x16_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_32x32_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_4x4_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_64x64_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_8x8_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_128x128_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_16x16_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_32x32_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_4x4_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_64x64_sites_1536x1000000_obs.tsv topological_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_8x8_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_128x128_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_16x16_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_32x32_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_4x4_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_64x64_sites_1536x1000000_obs.tsv zero_mode_susceptibility_ratio_elementary_electrolyte_8x8_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_128x128_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_16x16_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_32x32_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_4x4_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_64x64_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_sans_global_moves_8x8_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_128x128_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_16x16_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_32x32_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_4x4_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_64x64_sites_1536x1000000_obs.tsv zero_mode_susceptibility_vs_temperature_elementary_electrolyte_w_global_moves_8x8_sites_1536x1000000_obs.tsv ## Code/software The .tsv and .npy files were created using the GitHub repos super-aLby and xy-type-models.  These repos can be used to perform Monte Carlo simulations and then analyse the Monte Carlo outputs.   We did this using the HPC Avon of the Scientific Research Computing Technology Platform at the University of Warwick. To use the data contained in the .tsv and .npy files: 1. Clone the GitHub repositories [https://github.com/michaelfaulkner/super-aLby](https://github.com/michaelfaulkner/super-aLby) (commit hash 0ec5116) and [https://github.com/michaelfaulkner/xy-type-models](https://github.com/michaelfaulkner/xy-type-models) (commit hash 0adf8e7)  to your local working directory. 2. Follow the installation instructions in each README. 3. Create directories entitled output in super-aLby/src and xy-type-models. 4. Download this data deposit and add: 1. emergent_electrostatics_ising_figs to super-aLby/src/output 2. global_top_trace_plots and top_susc_figs to xy-type-models/output. 5. Follow the instructions relevant to the paper near the end of the super-aLby and xy-type-models README files, but... 6. ...IGNORE any instructions asking you to run simulations/configuration files, as this directory already contains the required data. If you have any questions, Michael Faulkner's contact details can be found at [https://github.com/michaelfaulkner](https://github.com/michaelfaulkner) and [https://orcid.org/0000-0002-9116-2878](https://orcid.org/0000-0002-9116-2878)