Estudo de transições de fases em um antiferromagneto frustrado utilizando Gilt-TNR

Abstract

We employ a recently proposed group of tensioner network called Gilt-TNR, scheme to estimate the critical temperature of the system as a function of the ratio between the coupling constants. Unlike the renormalization group of standard tensor (TRG), the new method is able to completely eliminate the correlations of short ange during the renormalization process. The technique is based on a representation of the system partition function by a network of tensor, in which each site in the network we associate a translationally invariant tensor. The tensor encodes the associated states degrees of freedom of the original system. The indexes of the tensors, which you call "legs", correspond to links between network sites. Thus, the calculation of the partition function is reduced to the contraction of a network of tensor. Here, we apply the technique to the Ising model defined in a square network with antiferromagnetic interactions between pairs first and second neighbors. In this case, the square network is completely frustrated. In the process of renormalizing the tensor network, we introduced a scale factor that prevents the limitless growth of the tensor norm. This scale factor captures the non-analyticity of free energy. Thus, the critical values of the parameters were obtained locating the point at which the scale factor presents a singularity. We examine values of the different frustration parameters R. We find the critical point for each value of R and determine the value of the critical exponents along the transition line. At analyzed region, we found no evidence of first-order phase transition or trichritic point.