| The phase transition of multi-body system is a difficult problem in physics.Numerical simulation is an important research tool in addition to theoretical and experimental research.From the point of view of simulation,the phase transition can be divided into equilibrium and non-equilibrium.The former needs to ensure that the system reaches a detailed balance in the evolution process,while the latter makes the characteristic time of external drive shorter than the relaxation time of the system,so that the system is driven to the next state before it has time to balance,which is also known as dynamical phase transition.Among many algorithms,the finite-time dynamical algorithm uses a finite time similar to finite size as a scale factor to detect the scale behavior of the system and extract the critical exponent and mark the universality class.Using this algorithm to simulate the phase transition behavior,the system can successfully cross the phase transition point under the driving of the external field and overcome the critical slowing down.The algorithm has been widely used in the dynamical simulation of phase transition phenomena.The aim of this paper is to parallelize the algorithm and obtain high speedup through programming to improve the simulation efficiency.The main contents and research results of this thesis are as follows:(1)In this paper,the finite-time dynamics algorithm is designed in parallel.Considering the advantages and disadvantages of different programming languages,parallel simulation algorithms based on Fortran+MPI and Python are implemented respectively.In addition,the effects of the size,number of samples,number of processes and temperature change rate of the simulation model on the parallel program acceleration ratio are studied in detail and measures to improve the speedup ratio are proposed.In order to avoid the time-consuming situation that the CPU waits for multiple data communication,each process stores the simulation result in a private array,and finally the primary process implements one-time data collection,which makes the parallel simulation system of this paper realize high simulation efficiency,when the number of processes is 10,an acceleration ratio of about 9.6 is obtained.(2)Using the parallel simulation system to simulate the two-dimensional Ising model,under the premise of improving the simulation efficiency,by increasing the size and sample number of the simulation model,the impact of the finite size effect is reduced as much as possible and a better sample average is obtained.It is found that the simulation results of each critical index agree with the theoretical values,which verifies the correctness of the parallel program.In addition,the three-dimensional Ising model has not been theoretically solved so far.In this paper,parallel simulation and research are carried out.After fitting by finite-time scale formula,it is found that each critical index is the same as that in most papers.(3)On the same workstation,the simulation time required for the two-dimensional and three-dimensional Ising models in the case of multi-sample and large-size is recorded respectively.Through comparison,it is found that under the same conditions,the running time and the rate of temperature change are almost strictly linear.In addition,at the same temperature change rate,the simulation time of the two-dimensional and three-dimensional Ising models can maintain a proportional relationship of nearly three times.Combined with the high acceleration ratio obtained before,it is proved that the parallel simulation system in this paper is suitable for parallel simulation operation of a certain scale,and the dimensional independence of Monte Carlo class algorithm is also proved.Finally,when the curve of simulated data is deviated and it is difficult to obtain a better statistical average by adding samples,this paper introduces the exponential weighted average algorithm to process the data,and obtains a smoother data curve with smaller deviation,so that a more accurate value can be obtained. |
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