Nonequilibrium Relaxation Method

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One well-established simulation strategy to study the thermal phases and transitions of a given microscopic model system is so-called the equilibrium method, in which one firstly realizes the equilibrium ensemble of a finite system and then extrapolates the results to infinite system. This equilibrium method traces over the standard theory of the thermal statistical mechanics, and over the idea of the thermodynamic limit. Recently, alternative simulation strategy has been developed by the initiative of the head investigator of this research project, which analyzes the nonequilibrium relaxation (NER) process. It is called the NER method. There are some advantages in the NER method over the equilibrium method. The NER method provides simpler analyzing procedure. This implies the less systematic error which is inevitable in the simulation and provides efficient resource usage. Main purpose of this research project is the following: (1) Further development of the NER method. (2) Refinement of the NER method as one standard technique to study material property. (3) Preparation towards analyzer software based on the NER method. During the four years of this project, these three are achieved. Analyzing method of the Kosterlitz-Thouless transition with the NER method is established, and it has turned out that hard-disk melting shows KT transition twice, as an example. Rejection free Monte Carlo method is developed for particle system, which makes simulation more efficient in high density region. An automatic analyzing software named as NER analyzer is designed and partly coded. The NER analyzer analyzes phase and exponent using the NER method by generating specified simulations, simulating and analyzing them, together with making precise log of execution in its database.