Monte Carlo critical isotherms for Ising lattices

TL;DR

This paper uses Monte Carlo simulations to accurately determine the critical exponent δ for Ising lattices in one to four dimensions, providing precise numerical values that are rarely reported in literature.

Contribution

It presents a novel Monte Carlo approach to directly measure the critical exponent δ for Ising lattices across multiple dimensions with high precision.

Findings

δ_{1D}^{-1} = 0 (δ_{1D} = ∞)

δ_{2D}^{-1} ≈ 1/15

δ_{3D}^{-1} ≈ 1/5

Abstract

Monte Carlo investigations of magnetization versus field, $M_c(H)$, at the critical temperature provide direct accurate results on the critical exponent $\delta^{-1}$ for one, two, three and four-dimensional lattices: $\delta_{1D}^{-1}$=0, $\delta_{2D}^{-1}$=0.0666(2)$\simeq$1/15, $\delta_{3D}^{-1}$=0.1997(4)$\simeq$1/5, $\delta_{4D}^{-1}$=0.332(5)$\simeq$1/3. This type of Monte Carlo data on $\delta$, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.