{"author":[{"first_name":"Ping","last_name":"Tuo","full_name":"Tuo, Ping","id":"6e5644c0-c180-11ed-a2da-facc4c9f4f09"},{"last_name":"Zeng","orcid":"0000-0001-5126-4928","first_name":"Zezhu","full_name":"Zeng, Zezhu","id":"54a2c730-803f-11ed-ab7e-95b29d2680e7"},{"orcid":"0000-0001-5337-5875","last_name":"Chen","first_name":"Jiale","id":"4d0a9064-1ff6-11ee-9fa6-ec046c604785","full_name":"Chen, Jiale"},{"orcid":"0000-0002-3584-9632","last_name":"Cheng","first_name":"Bingqing","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","full_name":"Cheng, Bingqing"}],"issue":"22","type":"journal_article","volume":21,"status":"public","oa_version":"None","month":"10","year":"2025","article_processing_charge":"No","related_material":{"link":[{"url":"https://github.com/tuoping/alchemicalFES","relation":"software"}]},"citation":{"ama":"Tuo P, Zeng Z, Chen J, Cheng B. Scalable multitemperature free energy sampling of classical Ising spin states. <i>Journal of Chemical Theory and Computation</i>. 2025;21(22):11427-11435. doi:<a href=\"https://doi.org/10.1021/acs.jctc.5c01248\">10.1021/acs.jctc.5c01248</a>","short":"P. Tuo, Z. Zeng, J. Chen, B. Cheng, Journal of Chemical Theory and Computation 21 (2025) 11427–11435.","apa":"Tuo, P., Zeng, Z., Chen, J., &#38; Cheng, B. (2025). Scalable multitemperature free energy sampling of classical Ising spin states. <i>Journal of Chemical Theory and Computation</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acs.jctc.5c01248\">https://doi.org/10.1021/acs.jctc.5c01248</a>","chicago":"Tuo, Ping, Zezhu Zeng, Jiale Chen, and Bingqing Cheng. “Scalable Multitemperature Free Energy Sampling of Classical Ising Spin States.” <i>Journal of Chemical Theory and Computation</i>. American Chemical Society, 2025. <a href=\"https://doi.org/10.1021/acs.jctc.5c01248\">https://doi.org/10.1021/acs.jctc.5c01248</a>.","mla":"Tuo, Ping, et al. “Scalable Multitemperature Free Energy Sampling of Classical Ising Spin States.” <i>Journal of Chemical Theory and Computation</i>, vol. 21, no. 22, American Chemical Society, 2025, pp. 11427–35, doi:<a href=\"https://doi.org/10.1021/acs.jctc.5c01248\">10.1021/acs.jctc.5c01248</a>.","ieee":"P. Tuo, Z. Zeng, J. Chen, and B. Cheng, “Scalable multitemperature free energy sampling of classical Ising spin states,” <i>Journal of Chemical Theory and Computation</i>, vol. 21, no. 22. American Chemical Society, pp. 11427–11435, 2025.","ista":"Tuo P, Zeng Z, Chen J, Cheng B. 2025. Scalable multitemperature free energy sampling of classical Ising spin states. Journal of Chemical Theory and Computation. 21(22), 11427–11435."},"title":"Scalable multitemperature free energy sampling of classical Ising spin states","publisher":"American Chemical Society","article_type":"original","quality_controlled":"1","intvolume":"        21","doi":"10.1021/acs.jctc.5c01248","corr_author":"1","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"publication":"Journal of Chemical Theory and Computation","external_id":{"pmid":["41172130"],"isi":["001605927900001"]},"date_published":"2025-10-31T00:00:00Z","publication_status":"published","scopus_import":"1","day":"31","abstract":[{"text":"Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In this work, we introduce a discrete flow matching model, tailored for systems with discrete phase-space coordinates (e.g., the Ising model or a multicomponent system on a lattice). This approach enables a single model to sample free energy surfaces over a wide temperature range with minimal training overhead, and the model generation is scalable to larger lattice sizes than those in the training set. We demonstrate our approach on the 2D Ising model, showing efficient and reliable free energy sampling. These results highlight the potential of flow matching for low-cost, scalable free energy sampling in discrete systems and suggest promising extensions to alchemical degrees of freedom in crystalline materials. The codebase developed for this work is openly available at https://github.com/tuoping/alchemicalFES.","lang":"eng"}],"acknowledgement":"P.T. acknowledges funding from FFG MAGNIFICO and the BIDMaP Postdoctoral Fellowship. Z.Z. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413. The authors acknowledge the research computing facilities provided by the Institute of Science and Technology Austria (ISTA), and resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award DOEERCAP0031751 ’GenAI@NERSC’. P.T. acknowledges valued discussions with Dr. Daniel King, Dr. Lei Wang, and Dr. Fuzhi Dai.","department":[{"_id":"BiCh"},{"_id":"DaAl"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-12-01T15:40:27Z","date_created":"2025-11-30T23:02:06Z","_id":"20704","pmid":1,"page":"11427-11435","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1549-9618"],"eissn":["1549-9626"]},"ec_funded":1,"acknowledged_ssus":[{"_id":"ScienComp"}],"OA_type":"closed access","isi":1}