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Spin glass theory, as a paradigm for describing disordered magnetic systems,constitutes a prominent subject of study within statistical physics. Replicasymmetry breaking (RSB), as one of the pivotal concepts for the understandingof spin glass theory, means that, under identical conditions disordered systemscan yield distinct states with nontrivial correlations. Random fiber laser(RFL) based on Rayleigh scattering (RS) is a complex disordered system, owingto the disorder and stochasticity of RS. In this work, for the first time, weelaborate a precise theoretical model for studying the photonic phasetransition via the platform of RS-based RFL, in which we clearly reveal that,apart from the pump power, the photon phase variation in RFL is also an analogyto the temperature term in spin glass phase transition, leading to a novelinsight into the intrinsic mechanisms of photonic phase transition. Inaddition, based on this model and real-time high-fidelity detection spectralevolution, we theoretically predict and experimentally observe themode-asymmetric characteristics of photonic phase transition in RS-based RFL.This finding contributes to a deeper understanding of the photonic RSB regimeand the dynamics of RS-based RFL.

Replica symmetry breaking in 1D Rayleigh scattering system: theory and validations