{"arxiv_id":"2103.12554","incoming":{"papers":8,"sentences":8,"groups":[{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2109.09555","title":"Learning quantum phase transitions through Topological Data Analysis","url":"/paper/2109.09555","section":"Introduction","sentence":"In order to provide their usefulness to examine phase transitions, many techniques, such as principal component analysis (PCA) [ref] , t-SNE [ref] , convolutional neural networks [ref] , restricted Boltzmann machines [ref] , intrinsic dimension analysis [ref] , and persistence homology [ref] , have been used to identify the critical points in effective (spin and/or fermionic) models.","intent_p":0.81,"contests_p":null},{"arxiv_id":"2312.04959","title":"Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis","url":"/paper/2312.04959","section":"Introduction","sentence":"In the related context of phase transitions, persistent homology allowed for insights into critical phenomena and phase structures [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":6},"outgoing":{"papers":24,"sentences":35,"groups":[{"kind":"extends","label":"Builds on","papers":1,"sentences":1,"quotes":[{"arxiv_id":"hep-lat/0101012","title":"Solution of the Complex Action Problem in the Potts Model for Dense QCD","url":"/paper/hep-lat/0101012","section":"Map of chemical potential to external field","sentence":"To make the Potts model relate to QCD, we here consider following extension of the Potts energy based on Ref. [ref] ; [equation] where $N_f$ denotes the number of flavor where we assume all favors are degenerated, $h_±$ is the external field explained in Eq. ([ref]) and $Φ_x$ ($Φ̅_x$) does the $ℤ_3$ values (its conjugate) on each site shown in Eq. ([ref]); it corresponds to the Polyakov-loop in QCD where the number of color is set to $3$.","intent_p":0.81,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1810.07635","title":"Persistent homology analysis of deconfinement transition in effective Polyakov-line model","url":"/paper/1810.07635","section":"Ratio of birth and death times","sentence":"To simply visualize the persistent diagram, the averaged ratio of the birth and death times has been proposed in Ref. [ref] ; [equation] where $N_h$ is number of all possible holes and $∑_i$ means that we sum up $t_D/t_B$ for all possible holes.","intent_p":0.89,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1103.5480","title":"Universality of Phases in QCD and QCD-like Theories","url":"/paper/1103.5480","section":"Introduction","sentence":"The important point is that it is known that the $μ_R$ region and the $μ_iso$ region are equivalent in the region where the pion condensation does not appear at least in the large $N_c$ limit; see Ref. [ref] as an example.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":12,"sentences":12,"quotes":[{"arxiv_id":"hep-lat/0101012","title":"Solution of the Complex Action Problem in the Potts Model for Dense QCD","url":"/paper/hep-lat/0101012","section":"Formalism","sentence":"In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.","intent_p":0.8,"contests_p":null},{"arxiv_id":"2009.12067","title":"Information theoretical view of QCD effective model with heavy quarks","url":"/paper/2009.12067","section":"Formalism","sentence":"In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.","intent_p":0.8,"contests_p":null},{"arxiv_id":"hep-lat/0510069","title":"The 3-state Potts model as a heavy quark finite density laboratory","url":"/paper/hep-lat/0510069","section":"Formalism","sentence":"In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1810.07635","title":"Persistent homology analysis of deconfinement transition in effective Polyakov-line model","url":"/paper/1810.07635","section":"Persistent homology analysis","sentence":"If the reader is interested in mathematical details of the persistent homology, see the text and conceptual figures in Sec. II of Ref. [ref] and references therein.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1411.4959","title":"Complex Saddle Points and Disorder Lines in QCD at finite temperature and density","url":"/paper/1411.4959","section":"Complexification in QCD","sentence":"It is well known that the $CK$ symmetry imposing on the Dirac operator can sidestep the sign problem at least in the mean-field level computation of the Nambu–Jona-Lasinio (NJL) type QCD effective model which includes the Polyakov-loop dynamics [ref] .","intent_p":0.84,"contests_p":null}]}],"unlabelled_sentences":20},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2103.12554"}}