The conditional second moment method used in this work has certain limitations, particularly in its applicability to a broader temperature regime. One limitation is the reliance on specific conditions and assumptions that may not hold universally across all temperature ranges. Additionally, the method may not capture the full complexity of the system dynamics, especially in regions where non-linear effects or phase transitions occur.
To cover a broader temperature regime, alternative approaches could involve incorporating higher-order moments, exploring different conditioning techniques, or utilizing advanced mathematical frameworks such as renormalization group methods. These approaches may offer a more comprehensive understanding of the system's behavior across various temperature ranges and could provide insights into the critical behavior of the model beyond the high-temperature regime.