Rydberg atom arrays have emerged as a powerful platform for experimental research and a challenging subject for theoretical investigation in quantum science. In this study, we investigate the finite-temperature properties of two-dimensional square-lattice Rydberg atom arrays using the projected entangled pair states (PEPS) method. By analyzing the thermal behavior of systems in the checkerboard and striated phases, we extract critical exponents and identify phase transition characteristics. Our results confirm that the checkerboard phase transition belongs to the 2D Ising universality class, while the striated phase exhibits critical exponents that deviate from known universality classes, possibly due to finite-size effects. These findings provide theoretical insights into the thermal stability of quantum phases in Rydberg atom arrays and offer valuable guidance for future experimental efforts.

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• Dipolar Rydberg atoms
• Phase transitions
• Transition temperature
• Rydberg atoms & molecules
• Strongly correlated systems
• Numerical techniques
• Tensor network methods