相关论文: Exact blocking formulas for spin and gauge models
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
We propose a new Real Space Renormalization Group transformation useful for Monte Carlo calculations in theories with global or local symmetries. From relaxation arguments we define the block-spin transformation with two tunable free…
We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the…
We investigate the Exact Renormalization Group (ERG) description of ($Z_2$ invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice.…
The exact renormalisation group equation is studied for a two-dimensional theory with exponential interaction and a background charge at infinity. The motivation for studying this interaction is the flow between unitary minimal models…
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…
We present a new family of zero-field Ising models over $N$ binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components and subsets of at most three vertices into a tree. The polynomial-time algorithm of…
We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the…
We construct a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills theory, in a form suitable for calculations without gauge fixing at any order of perturbation theory. The effective cutoff is incorporated via a…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to do explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the…
We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising…
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm…
We construct a real space renormalization group (RG) approach for Ising spin glasses on hypercubic lattices within the scheme of the Migdal-Kadanoff approximation using replicas. Our replica symmetric solution yields results consistent with…
A new block spin renormalization group transformation for SU(N) gauge models is proposed near the non-trivial fixed point in perturbation theory and thereby the expectation values of various Wilson loops on the renormalized trajectory near…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…