human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "swendsen wang algorithm on the mean field potts model"):
  Abstract: We study the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation for the ferromagnetic Potts model to recolor large sets of vertices in one step and potentially overcomes obstacles that inhibit single-site Glauber dynamics. Long et al. studied the case $q=2$, the Swendsen-Wang algorithm for the mean-field ferromagnetic Ising model, and showed that the mixing time satisfies: (i) $\Theta(1)$ for $\beta \beta_c$, where $\beta_c$ is the critical temperature for the ordered/disordered phase transition. In contrast, for $q\geq 3$ there are two critical temperatures $0<\beta_u<\beta_{rc}$ that are relevant. We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the $n$-vertex complete graph satisfies: (i) $\Theta(1)$ for $\beta<\beta_u$, (ii) $\Theta(n^{1/3})$ for $\beta=\beta_u$, (iii) $\exp(n^{\Omega(1)})$ for $\beta_u<\beta<\beta_{rc}$, and (iv) $\Theta(\log{n})$ for $\beta\geq\beta_{rc}$. These results complement refined results of Cuff et al. on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.

Includes members:
  Member "random cluster dynamics for the ising model is rapidly mixing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "ferromagnetic potts model refined bis hardness and related results":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficient algorithms for the potts model on small set expanders")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DM(Discrete Mathematics)