The logarithmic susceptibility asymptotic for the four-dimensional Ising model

Let $\chi(\beta)$ denote the susceptibility of the high-dimensional Ising model and let $\beta_c$ be its critical inverse temperature. Logarithmic susceptibility conjecture. Let $d=4$. There exists $A>0$ such that

$$\chi(\beta)=\frac{A|\log (1-\beta/\beta_c)|^{1/3}}{1-\beta/\beta_c}(1+o(1)),$$

where $o(1)$ tends to $0$ as $\beta$ tends to $\beta_c$. Renormalization group analysis and universality suggest this four-dimensional logarithmic correction to mean-field susceptibility behavior; the statement remains open in the source.