Researches for Applications of Nonequilibrium Relaxation Analysis and KT-transition Systems

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The nonequilibrium relaxation (NER) method is a numerical tool to investigate equilibrium phase transitions. Previously, we have shown that the method provides the transition temperature and critical exponents accurately for second-order phase transition systems. It reveals reliable results on systems on very large sizes which can not be treated by equilibrium simulations. One of remarkable features is that it can treat slowly-relaxing systems such as frustrated and/or random systems with high efficiency and high accuracy.In the present study, we extend the NER method to various types of phase transitions instead of second-order one ; especially for the Kosterlitz-Thouless transition, in which a critical behavior appears whole in the low-temperature regime and standard analyses used in the second-order transitions have not worked well.We have established a general procedure to estimate the KT-transition temperature. It has applied to various KT-systems such as the two dimensional hard-disk system. We also have established a procedure to estimate critical exponents for KT-transition, which provides a systematic investigation of the universality for KT-transitions. We also investigated the two dimensional Villain model with both continuous symmetry and 6-clock symmetry, which lead us to a discussion for the universality. We have proposed a relaxation process to estimate the transition temperature precisely for first-order phase transitions ; this is called the "mixed phase initialization". We have applied this initialization to the hard-sphere model and liquid crystal systems, in which the efficiency of the method has been confirmed.