Ising spins coupled to a four-dimensional discrete Regge skeleton

Abstract

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.

19 pages, 7 figures

References in corpus (1)

• Spins coupled to a $Z_2$-Regge lattice in 4d

Cited by in corpus (16)

• Nonlocal Effective Gravitational Field Equations and the Running of Newton's G
• Critical behaviour of the Ising model on the 4-dimensional lattice
• Analogue models for FRW cosmologies
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Non-Perturbative Gravity and the Spin of the Lattice Graviton
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Exploration of the phase diagram of 5D anisotropic SU(2) gauge theory
• The square-lattice F model revisited: a loop-cluster update scaling study
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
• Universality, vortices and confinement: modified SO(3) lattice gauge theory at non-zero temperature
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Revising the universality class of the four-dimensional Ising model
• Teleparallel gravity on the lattice
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna