Ising spins coupled to a four-dimensional discrete Regge skeleton

TL;DR

This paper investigates the phase transition behavior of Ising spins coupled to a four-dimensional discrete Regge skeleton, using Monte Carlo simulations to analyze critical phenomena and compare with mean-field predictions.

Contribution

It introduces a coupling of spins to fluctuating four-dimensional Regge manifolds and analyzes the resulting phase transition properties.

Findings

Results are consistent with mean-field theory predictions.

Finite-size scaling analyses support the critical behavior observed.

Coupling to fluctuating manifolds influences the phase transition characteristics.

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.