Universality of the complete-graph Potts model with $0<q\le 2$

Abstract

Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of microscopic details. In a simplest and mean-field treatment--i.e., the Potts model on complete graph (CG), the phase transition is further established to be of percolation universality for the range of $0<q<2$. By simulating the CG Potts model in the random-cluster representation, we numerically demonstrate such a hyper-universality that the critical exponents are the same for $0<q<2$ and, moreover, the Ising system ($q=2$) exhibits a variety of critical geometric properties in percolation universality. On the other hand, many other universal properties in the finite-size scaling (FSS) theory, including Binder-like ratios and distribution function of the order parameter, are observed to be $q$-dependent. Our finding provides valuable insights for the study of critical phenomena in finite spatial dimensions, particularly when the FSS theory is utilized.

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• Kinetic Theory of Random Graphs: from Paths to Cycles
• The Binder Cumulant at the Kosterlitz-Thouless Transition
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• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Geometric properties of the complete-graph Ising model in the loop representation
• Universality of the complete-graph Potts model with $0<q\le 2$
• Sweeny dynamics for the random-cluster model with small $Q$

Cited by in corpus (1)

• Universality of the complete-graph Potts model with $0<q\le 2$