The paper introduces a new spatial block-correlation model for fluid antenna systems (FAS), which are emerging technologies enabling massive connectivity in 6G networks. The model aims to address the high spatial correlation between antenna elements in FAS, which can lead to significant interference and limit the system's performance. The proposed model approximates the spatial correlation matrix using block-diagonal matrices, inspired by the block-fading assumption and statistical results on large Toeplitz matrices. This approach provides a balance between accuracy and mathematical tractability, making it suitable for analyzing FAS systems, particularly slow-FAMA systems. The paper begins by reviewing classical channel models and spatial correlation models, highlighting the limitations of existing models in terms of complexity and accuracy. It then proposes a block-diagonal spatial correlation model that captures the spectral characteristics of any correlation function, including realistic models like Jakes's and Clarke's. The model is derived using spectral analysis of large Toeplitz matrices, showing that the correlation matrix is dominated by a few eigenvalues, which can be approximated by block-diagonal matrices. The block-diagonal approximation is applied to slow-FAMA systems, where the outage probability (OP) is evaluated using tractable expressions. The model is validated through simulations, demonstrating its effectiveness in capturing the multiplexing capabilities of FAS. The paper also discusses the impact of fluid antenna size, the saturation effect, and the number of simultaneous users supported by the system. The derived approximations for the OP are shown to capture these effects accurately. Overall, the proposed block-diagonal spatial correlation model offers a practical and accurate framework for analyzing FAS systems, providing insights into their performance and potential benefits over conventional antenna systems.The paper introduces a new spatial block-correlation model for fluid antenna systems (FAS), which are emerging technologies enabling massive connectivity in 6G networks. The model aims to address the high spatial correlation between antenna elements in FAS, which can lead to significant interference and limit the system's performance. The proposed model approximates the spatial correlation matrix using block-diagonal matrices, inspired by the block-fading assumption and statistical results on large Toeplitz matrices. This approach provides a balance between accuracy and mathematical tractability, making it suitable for analyzing FAS systems, particularly slow-FAMA systems. The paper begins by reviewing classical channel models and spatial correlation models, highlighting the limitations of existing models in terms of complexity and accuracy. It then proposes a block-diagonal spatial correlation model that captures the spectral characteristics of any correlation function, including realistic models like Jakes's and Clarke's. The model is derived using spectral analysis of large Toeplitz matrices, showing that the correlation matrix is dominated by a few eigenvalues, which can be approximated by block-diagonal matrices. The block-diagonal approximation is applied to slow-FAMA systems, where the outage probability (OP) is evaluated using tractable expressions. The model is validated through simulations, demonstrating its effectiveness in capturing the multiplexing capabilities of FAS. The paper also discusses the impact of fluid antenna size, the saturation effect, and the number of simultaneous users supported by the system. The derived approximations for the OP are shown to capture these effects accurately. Overall, the proposed block-diagonal spatial correlation model offers a practical and accurate framework for analyzing FAS systems, providing insights into their performance and potential benefits over conventional antenna systems.