Related papers: Optimal Real-Space Renormalization-Group Transform…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum…
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…
Three dimensional Ising model ferromagnets on different lattices with nearest neighbor interactions, and on simple cubic lattices with equivalent interactions out to further neighbors, are studied numerically. The susceptibility data for…
We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field. Our method is…
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto…
We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes,…
We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the…
In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct…
We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum…
We explore alternative experimental setups for the iterative sampling (flow) from Restricted Boltzmann Machines (RBM) mapped on the temperature space of square lattice Ising models by a neural network thermometer. This framework has been…
We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…
Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea…
The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension $\log_{4} 12 \approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…