Tensor renormalization of three-dimensional Potts model

Abstract

We study the q-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase transitions for 10 < q ≤ 20 which has not been explored using any method. We also examine the efficiency of the triad approximation method in obtaining the fixed-point tensor and comment on how this can be improved.

Gpu-Acceleration of Tensor Renormalization with Pytorch Using Cuda

“…In an earlier work by one of the authors [10], to perform the most expensive part of the computationstensor contractions, the ncon Python library was used. There is an equivalent way of doing these contractions which has been extensively used in machine learning and is known as opt_einsum [11] which was used for standard CPU computations in [12]. In this work, we make use of additional capabilities of opt_einsum by performing these contractions on a GPU architecture without explicitly copying any tensor to GPU device.…”

“…The q-state Potts model has been previously considered using TRG methods both in two and three dimensions in Refs. [12,21]. The initial tensor can be written down by considering the q × q Boltzmann nearest-neighbor weight matrix as:…”