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In public spaces shared with humans, ensuring multi-robot systems navigate without collisions while respecting social norms is challenging, particularly with limited communication. Although current robot social navigation techniques leverage advances in reinforcement learning and deep learning, they frequently overlook robot dynamics in simulations, leading to a simulation-to-reality gap. In this paper, we bridge this gap by presenting a new multi-robot social navigation environment crafted using Dec-POSMDP and multi-agent reinforcement learning. Furthermore, we introduce SAMARL: a novel benchmark for cooperative multi-robot social navigation. SAMARL employs a unique spatial-temporal transformer combined with multi-agent reinforcement learning. This approach effectively captures the complex interactions between robots and humans, thus promoting cooperative tendencies in multi-robot systems. Our extensive experiments reveal that SAMARL outperforms existing baseline and ablation models in our designed environment. Demo videos for this work can be found at: https://sites.google.com/view/samarl