This paper investigates the decentralized detection of spatially correlated processes using the Neyman-Pearson test. We consider a network formed by a large number of sensors, each of them observing a random data vector. Sensors' observations are non-independent, but form a stationary process verifying mixing conditions. Each vector-valued observation is quantized before being transmitted to a fusion center which makes the final decision. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of sensors tends to infinity. A compact closed-form expression of the error exponent is provided in the high-rate regime i.e., when fine quantization is applied. As an application, our results allow to determine relevant quantization strategies which lead to large error exponents.