2010/04/30 by T. Machado, Tamires Martinhão Machado, N. Dupuis · 1 citation
Physics and Astronomy · #Classical XY model #Critical dimension #Critical phenomena #Ising model #Lattice (music) #Lattice field theory #Lattice model (finance) #Mathematical physics #Mean field theory #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physreve.82.041128
published as Phys. Rev. E 82, 041128 (2010) · v1) 12 pages, 12 figures. v2) Revised version. v3) Improved figures
openalex publication_date 2010/10/28 · arxiv created 2010/11/15 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose an implementation of the nonperturbative renormalization group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses the (local) limit of decoupled sites as the (initial) reference system. In the long-distance limit, it is equivalent to the usual NPRG formulation and therefore yields identical results for the critical properties. We discuss both a lattice field theory defined on a d-dimensional hypercubic lattice and classical spin models. The simplest approximation, the local potential approximation, is sufficient to obtain the critical temperature and the magnetization of the three-dimensional Ising, XY, and Heisenberg models to an accuracy on the order of 1%. We show how the local potential approximation can be improved to include a nonzero anomalous dimension η and discuss the Berezinskii-Kosterlitz-Thouless transition of the two-dimensional XY model on a square lattice.