<p>Cyclic liquid nitrogen (LN₂) and nitrogen gas (N₂) fracturing is an innovative technique using cryogenic LN₂ and normal-temperature N₂ as the fracturing fluid, crucial for efficient deep hot dry rock (HDR) development. This study establishes a phase-field cohesive zone model (PF-CZM) with thermo-hydro-mechanical (THM) coupling. The model fully accounts for the physical properties of nitrogen related to temperature and pressure. The model’s reliability is validated using experimental and numerical results. Based on the proposed model, the intersection mechanism of fractures induced by LN₂-N₂ fracturing with natural fractures is revealed. Additionally, the spatially heterogeneous fields with varying variance are generated based on the turning bands theory to characterize the mechanical and seepage parameters of granite. The influence of LN₂-N₂ cycle number, heterogeneity degree, and in-situ stress on fracture propagation is systematically analyzed. Research results indicate that the initiation and breakdown pressures of LN₂ fracturing are 73.5% and 42.1% lower, respectively, than those of N₂ fracturing under the same conditions. Appropriately increasing the number of fracturing cycles promotes cumulative damage within the granite. With a higher degree of heterogeneity, cyclic fracturing leads to a significant reduction in both initiation and breakdown pressures. This reduction in the initiation pressure is more pronounced and exhibits a stronger dependence on heterogeneity. Furthermore, an increase in in-situ stress difference reduces both initiation and breakdown pressure. These findings provide a theoretical foundation and practical guidance for optimizing process parameters in the LN₂-N₂ fracturing of HDR geothermal reservoirs.</p>