Universal amplitude ratios in the three-dimensional Ising universality class

We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain $A_{+}/A_{-}=0.536\left(2\right)$ and $C_{+}/C_{-}=4.713\left(7\right)$, where $A_{\pm }$ and $C_{\pm }$ are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts $+$ and $-$ indicate the high- and the low-temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high- and low-temperature series expansions, field theoretic methods, and experiments.

Figure 1

We plot the ratio $\chi \left(t\right)/\chi \left(-t\right)$ as a function of $t={\beta }_c-\beta$ computed from our data for $D=0.655$. For a discussion see the text.

Figure 2

We plot the ratio $u\left(t\right)=3\chi \left(t\right)/{\xi }_{2nd}^3\left(t\right)m^2\left(t\right)$ as a function of $-t=\beta -{\beta }_c$ computed from our data for $D=0.655$. For a discussion see the text.