Numerical Simulation And FPGA Implementation Of The Ising Model

Phase transition, is a kind of break phenomena which exits in the nature widely, is akind of transition process in which substance system changes from one steady state toanother, and is an important research area in Physics. Ising model is abstracted from themagnetic system,which describes a simple model of the material phase transitions andcritical phenomena.Compared to software implementation, implementation throughhardware is faster.Therefore, adopting the method of hardware to complete the simulationof Ising model has a more important value and significance. This paper mainly analyzesthe results of Ising model which is generated by Monte Carlo’s method and cellularautomata method,then designs and realizes the simulation of cellular automata of Isingmodel by FPGA. At last,it compares and analyzes the experiment result.Firstly,it presents domestic and overseas research on Ising model at present and alsointroduces the exact solution to one-dimensional and two-dimensional models,thenanalyzes the difficulties in the study on the exact solution to three-dimensional model.Moreover, numerical simulation method set by Monte Carlo and renormalization groupmethod are used to summarize the results of work on Ising model.Secondly, the numerical simulation of cellular automata of Ising model are discussedin this paper. The cellular automata and simulation of physical systems are formulated.Furthermore, the principles and methods of cellular automata of Ising model are describedin detail. Based on the information obtained from the cellular automata’s simulation resultsof two-dimensional Ising model which achieved through software,this article gets thecritical value of system energy when the phase transformations and macroscopicmagnetization are generated.Finally,with the method combining schematic input method and Verilog HDLlanguage,it achieves the cellular automata’s simulation to one-dimensional andtwo-dimensional models,then uses QuartusⅡ software to realize the comprehensivesimulation and download to the evaluation board. Through the comparison of the resultsbetween two-dimensional simulation and software method,it demonstrates thatimplementation of parallel method is superior to that of software method.