Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet

The possibility of the emergence of some kind of long-range ordering (LRO) due to the increase of multiplicity of the local degrees of freedom (spin value $S$) is studied in an Ising antiferromagnet on a kagome lattice (IAKL) by Monte Carlo simulation. In particular, the critical exponent of the spin correlation function, obtained from a finite-size scaling analysis, is evaluated for various values of $S$, including $S=\infty$, with the goal to determine whether there exists some threshold value of the spin $S_C$ above which the system would show true or quasi-LRO, similar to a related model on a triangular lattice (IATL). It is found that, unlike in the IATL case, the IAKL model remains disordered for any spin value and any finite temperature.