There is a research field called a fluctuating system. In systems such as Brownian motion, the particles of interest exchange kinetic energy from white noise and perform a random walk. The Langevin equation handles these events and takes up fine particle friction and microwave irradiation to confirm the operation of the system. In this paper, we incorporate microwave irradiation into the Maxwell-Boltzman distribution and confirm that its non-thermal energy exhibits the so-called "microwave effect". Non-thermal energy from microwaves has the effect of accelerating the reaction speed of system phase transitions and chemical changes. Also, when observing one particle, the correlated noise is described as a function of time, and the change in kinetic energy is described. The effect of correlated noise is not seen when observing many particles, but it is important that it appears when observing one particle, and it has a wide range of applications such as phase transitions and chemical changes. A two-dimensional Ising model is proposed as a specific example of Monte Carlo simulation using noise. Results will vary depending on the strength of the noise-to-noise correlation. In this way, the noise-to-noise correlation has a strong effect on physical quantities.