[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126524-en":3,"doc-seo-126524-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126524,962085662650,"Jiven","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine learning phase transitions of the three-dimensional Ising universality class","Machine learning techniques are applied to study phase transitions in the three-dimensional (3D) cubic Ising model under a supervised learning framework, motivated by the expectation that the QCD critical point belongs to the 3D Ising universality class. A 3D convolutional neural network is trained to predict physical quantities across different spin configurations. Using a uniform architecture, the model encodes phases of matter and distinguishes both second- and first-order phase transitions. Discriminating features are analyzed to support investigations of QCD phase transitions in relativistic heavy-ion collisions.","Machine learning phase transitions of the three-dimensional Ising universality class  \narXiv :2112 . 13987v2 [nucl-th] 18 Jul 2022  \nXiaobing Li, 1 Ranran Guo, 1 Yu Zhou,2 Kangning Liu, 1 Jia Zhao, 1 Fen Long, 1 Yuanfang Wu, 1 and Zhiming Li 1, 􀀃  \n1 Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics,  \nCentral China Normal University, Wuhan 430079, China  \n2 University of California, Los Angeles, CA 90095, USA  \nExploration of the QCD phase diagram and the critical point is one of the main goals in current relativistic heavy-ion collisions. The QCD critical point is expected to belong to a three-dimensional  \n(3D) Ising universality class. Machine learning techniques are found to be powerful in distinguishing di􀀋erent phases of matter and provide a new way on the study of phase diagram. We investigate phase transitions in the 3D cubic Ising model by using supervised learning methods. It is found that a 3D convolutional neural network can be trained to well predict physical quantities in di􀀋erent spin con􀀌gurations. With a uniform neural network architecture, it can encode phases of matter and identify both the second- and the 􀀌rst-order phase transitions. The important features that discriminate di􀀋erent types of phase transitions in the classi􀀌cation processes are investigated. These  \n􀀌ndings could help to study and understand the QCD phase transitions in relativistic heavy-ion  \ncollisions.  \nI. INTRODUCTION  \nOne of the major goals in high energy heavy-ion collisions is to explore the QCD phase structure and the critical point [1{4] . Due to the fermion sign problem, Lattice QCD calculation is restricted to the region of vanishing or small baryon chemical potential (􀀖B ) and it predicts acrossover from hadronic phase to a Quark Gluon Plasma (QGP) phase in this area [5, 6] . The results of QCD based models indicate that the transition could be a 􀀌rst-order at large 􀀖 B [7] . The point where the 􀀌rst-order phase transition ends is the critical point (CP) [8, 9] . This CP is proposed to be characterized by a second-order phase transition, which becomes a unique property of strongly interacting matter [10{13] . Attempts are being made to explore the CP and phase boundary both experimentally and theoretically [10{21] .  \nThe QCD equation of state with a CP is an essential ingredient for hydrodynamic simulations of 􀀌reball evolution in heavy-ion collision. Universality of critical phenomena allows us to predict the leading singularity of the QCD equation of state near CP [21] . Systems with di􀀋erent interactions, but with the same symmetry structure and having the same dimensionality, share the same critical behaviour. It is argued that the QCD CP belongs to the same Z(2) universality class [22, 23] as the threedimensional (3D) Ising model [1, 24{27] . Therefore, universality makes the Ising model very relevant for studies of systems that display the Z(2) symmetry [28{31] . By means of a parametrization of the scaling equation of state in the 3D Ising model and a non-universal mapping, it allows to construct an equation of state matching the 􀀌rst principle Lattice QCD calculations and to include the proper scaling behavior in the proximity of the CP [11, 32{35] . It can also map the phase diagram of the 3D Ising model onto the one of QCD [32, 36 , 37] .  \n􀀃 Electronic address: [lizm@mail.ccnu.edu.cn](lizm@mail.ccnu.edu.cn)  \nThus the CP, the lines of 􀀌rst-order phase transition and crossover in the 3D Ising model are related to those of QCD.  \nClassifying phases of matter and identifying phase transitions is one of the central topics in current phase structure investigations. In the conventional statistical method, it relies on the identi􀀌cation of order parameters or the analysis of singularities in the free energy and its derivatives. However, the order parameter of the QCD phase transition is hard to determine or di􀀎cult to measure in experiments. And some phases like topological ones [38, 39]","cbCaic54q6aI1YwS","https://ap.wps.com/l/cbCaic54q6aI1YwS","pdf",652774,1,7,"English","en",105,"# Introduction\n## QCD phase structure and critical point\n## Universality and mapping to the 3D Ising model\n## Motivation for ML-based phase classification","[{\"question\":\"Why does the QCD critical point relate to the 3D Ising universality class?\",\"answer\":\"Universality of critical phenomena implies that systems with the same symmetry structure and dimensionality share the same critical behavior. The QCD critical point is proposed to belong to the same Z(2) universality class as the 3D Ising model.\"},{\"question\":\"How is machine learning used to investigate phase transitions in the 3D Ising model?\",\"answer\":\"The study uses supervised learning on phase-transition data from the 3D cubic Ising model. A 3D convolutional neural network is trained to predict physical quantities from spin configurations.\"},{\"question\":\"Can the neural network distinguish different orders of phase transitions?\",\"answer\":\"Yes. With a uniform neural network architecture, it encodes phases of matter and identifies both second-order and first-order phase transitions, and the work also investigates discriminating features for the classification.\"}]","Machine learning phase transitions of the three-dimensional Ising universality class | PDF",1785933142,18,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"machine-learning-phase-transitions-of-the-three-dimensional-ising-universality-class","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-phase-transitions-of-the-three-dimensional-ising-universality-class/126524/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why does the QCD critical point relate to the 3D Ising universality class?","Question",{"text":76,"@type":77},"Universality of critical phenomena implies that systems with the same symmetry structure and dimensionality share the same critical behavior. The QCD critical point is proposed to belong to the same Z(2) universality class as the 3D Ising model.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How is machine learning used to investigate phase transitions in the 3D Ising model?",{"text":81,"@type":77},"The study uses supervised learning on phase-transition data from the 3D cubic Ising model. A 3D convolutional neural network is trained to predict physical quantities from spin configurations.",{"name":83,"@type":74,"acceptedAnswer":84},"Can the neural network distinguish different orders of phase transitions?",{"text":85,"@type":77},"Yes. 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