Percolation and finite size scaling in seven dimensions

TL;DR

This paper investigates critical exponents in percolation and Ising models in seven dimensions, revealing differences in phase transition behaviors above the critical dimension through extensive numerical simulations.

Contribution

It provides new insights into the distinct nature of phase transitions in high-dimensional systems, especially above the critical dimension.

Findings

Percolation and Ising model phase transitions differ above the critical dimension.

Finite size scaling behavior varies with dimension.

Numerical results extend up to L=33 in seven dimensions.

Abstract

Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.