| Abstract: | Tensor networks provide a powerful framework for studying many-body systems and phase transitions. We explore how Tensor Network Renormalization Group methods can help characterize first- and second-order phase transitions. Using the HOTRG method, we study the 2D Blume-Capel model, by constructing a tensor network representation of its partition function and iteratively applying an RG transformation to simulate exponentially large systems. We compute and analyze thermodynamic observables and tensor spectra to distinguish between different phases and transition orders. Additionally, we locate the tricritical point by identifying the critical behavior of the tensor spectrum in its vicinity and extract critical exponents via finite-size scaling. Our results provide insights into phase transition behavior using tensor network techniques. |