Nonequilibrium relaxation analysis of fully frustrated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>models in two dimensions

Abstract

The nonequilibrium relaxation (NER) method is applied to the fully-frustrated $\mathrm{XY}$ models on square and triangular lattices. The transition temperatures of chiral and Kosterlitz-Thouless transitions are estimated with a high degree of precision on very large lattices. It is found that these two transitions occur at different temperatures for both models, which indicates the double transition and the existence of the intermediate phase. Further, we calculate the NER functions of fluctuations for chiral transition to estimate critical exponents. It is indicated that these models belong to the same universality class which is of different from the Ising class in two dimensions.