Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries

Abstract

We present an extensive Markov-chain Monte Carlo study of the finite-size scaling behavior of the Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodic boundary conditions. We observe that physical quantities, which include the contribution of the largest cluster, exhibit complete graph asymptotics. However, for quantities, where the contribution of the largest cluster is removed, we observe that the scaling behavior is mainly controlled by the Gaussian fixed point. Our results therefore suggest that \textit{both} scaling predictions, i.e. the complete graph \textit{and} the Gaussian fixed point asymptotics, are needed to provide a complete description for the five-dimensional finite-size scaling behavior on the torus.

arXiv comment7 pages, 7 figures

References in corpus (15)

• The Random-Cluster Model
• Hyperscaling above the upper critical dimension
• Finite-size scaling above the upper critical dimension
• Finite size scaling of the correlation length above the upper critical dimension
• On the role of Fourier modes in finite-size scaling above the upper critical dimension
• Fisher's scaling relation above the upper critical dimension
• Finite size scaling of the 5D Ising model with free boundary conditions
• Random-length Random Walks and Finite-size scaling in high dimensions
• Geometric explanation of anomalous finite-size scaling in high dimensions
• Critical percolation clusters in seven dimensions and on a complete graph
• Finite-Size Correlation Length and Violations of Finite-Size Scaling
• Geometric properties of the Fortuin-Kasteleyn representation of the Ising model
• The scaling window of the 5D Ising model with free boundary conditions
• Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary
• Two-point functions of random-length random walk on high-dimensional boxes

Cited by in corpus (11)

• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality
• Geometric Upper Critical Dimensions of the Ising Model
• Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions
• Quantum extraordinary-log universality of boundary critical behavior
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
• Universality of the complete-graph Potts model with $0<q\le 2$