The work of DM is supported by a studentship awarded by the Data Intensive Centre for Doctoral Training, which is funded by the STFC grant ST/P006779/1. The work of DV is partly supported by the Simons Foundation under the program "Targeted Grants to Institutes" awarded to the Hamilton Mathematics Institute. The work of BL and MP has been supported in part by the STFC Consolidated Grants No. ST/P00055X/1 and No. ST/T000813/1. BL and MP received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under Grant Agreement No.~813942. The work of BL is further supported in part by the Royal Society Wolfson Research Merit Award WM170010 and by the Leverhulme Trust Research Fellowship No. RF-2020-4619. Numerical simulations have been performed on the Swansea SUNBIRD cluster (part of the Supercomputing Wales project) and AccelerateAI A100 GPU system, and on the DiRAC Data Intensive service at Leicester. The Swansea SUNBIRD system and AccelerateAI are part funded by the European Regional Development Fund (ERDF) via Welsh Government. The DiRAC Data Intensive service at Leicester is operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC Data Intensive service equipment at Leicester was funded by BEIS capital funding via STFC capital grants ST/K000373/1 and ST/R002363/1 and STFC DiRAC Operations grant ST/R001014/1. DiRAC is part of the National e-Infrastructure.

Data release for paper: Lucini, B., Mason, D., Piai, M., Rinaldi, E., & Vadacchino, D. (2023). First-order phase transitions in Yang-Mills theories and the density of state method. arXiv preprint arXiv:2305.07463. This data release comprises of: Importance sampling results: Input and output files for PureGauge file of HiRep (https://github.com/claudiopica/HiRep) and csv files contains analysis of results. LLR results: Input files for LLR_HB for a modified version of HiRep for the heat bath LLR algorthim with umbrella sampling (https://github.com/dave452/Hirep-LLR-SU) and some csv files containing analysis of output. Analysis code within the LLRAnalysis.zip, it contains the code and the conda environment.