Utilizing multilayer networks to explore minority languages phase transitions

• we investigate and analyze the language usage in China's ethnic minority areas, which is the first time to reveal the use of minority languages. • The influence of different social relations on language evolution is quantitatively described by multilayer networks, and the threshold of language diffusion is well obtained by theoretical analysis and numerical experiments. • By real research data, we set up a real two-layer network and get the results consistent with the theoretical analysis. Studying the shift of linguistic states between intelligences is an important topic in information science. It is also one of the central topics in network science since the state of language communication between social individuals can be described using networks. Minority languages have a crucial role in preserving minority cultures but research on the diffusion mechanisms and empirical data in different social networks is lacking. We conduct a targeted household survey of 224 individuals in the minority Wa region of Yunnan Province, China, revealing different language usage patterns in ethnic group network and economically active network. We define a multilayer network framework to characterize the dynamics of minority language diffusion and analytically determine the dynamic phase transitions in language diffusion. We propose three types of interactions between the upper ethnic group network and the lower economically active network, positive interaction, negative interaction and neutral interaction, which have inverse effects on the language diffusion threshold. Through theoretical analysis and numerical simulations, the findings reveal that multi-layered heterogeneous networks, particularly in economically active contexts, can promote bilingualism. Furthermore, we illustrate social relationship networks in a real-world system, highlighting the positive interaction of the upper ethnic group network, the rate of language diffusion and the significance of network structure for minority language diffusion. This study reveals the dynamic diffusion mechanisms of minority languages across complex social relationships and provides a theoretical basis for developing strategies to preserve linguistic diversity.