The Evolution From Non-equilibrium To Equilibrium Of Two Dimensional Ising System

Quantum Chromodynamics(QCD)is a gauge theory that describes the strong inter-actions.It predicts that quarks confined in the hadron will be deconfined and form a quark glue plasma(QGP)at high enough energy.The phase transition from hadron to QGP is first-order phase transition at low-temperature and large baryon chemical potential region.And the end point of first order phase transition line is the critical point of QCD.At high temperature and low baryon chemical potential region,the hadron will smoothly transition to the critical point of QCD.For the infinite system,the correlation length and correlation time tend to be infinite,and the specific heat and susceptibility diverge near the critical point.As for the finite system,the correlation length,correlation time,and the specific heat are limited due to the finite scale effect.Moreover,the study show that high-order cumulants of the conserved charges(the number of baryons,the number of charges,the number of strangeness)are sensitive to the correlation length,which means the high-order cumulants can be used as a signal to search the critical point.We use the Metropolis algorithm to simulate the two-dimensional Ising system that will experience a transition from order to disorder with the increase of temperature in the zero magnetic field.At different temperature or different system size,the time required for the simulating system to reach equilibrium is different.When the temperature is close to Tc,the equilibrium time become large due to the critical fluctuation.After the system reaches equilibrium,we can selecte magnetization as sample to cal-culate the higher moments,and the interval of selecting samples depends on the correlation time ?.The correlation time ? is obtained by calculating the time-displacement autocor-relation function.Below Tc,? grows as the temperature increases.Above Tc,? decreases as the temperature increases.At T = Tc,there is a maximum.At the critical point,the correlation time increases with the increase of system size,which is critical slowing down.When the system size is close to infinite,at the critical point,its correalation time will be infinite,and the system hardly evolve to equilibration.Using the 2-D Ising model,we calculate the moments of the magnetization at van-ishing external field after selecting the appropriate sample.We find that the third-order moment,the fourth-order moment,and the sixth-order moment all have sign change at the critical point.The sixth-order moment even has two sign change behavior,In the terms of larger system,temperature corresponding to their sign change is closer to Tc.