A self-consistent renormalization scheme suitable for the calculation of non-universal quantities in $n$ -vector models with pair spin interactions of arbitrary extent has been suggested. The method has been based on the elimination of the fluctuating field components within the layers defined by the layer-cake representation of the propagator. The non-perturbative renormalization group (RG) equations has been solved in the local potential approximation. Critical temperatures of the $n=1-3$ vector spin models on cubic lattices have been calculated in excellent agreement with the best known estimates. Several critical amplitudes and the magnetisation curve of the Ising model on the simple cubic lattice calculated within the approach compared well with the values from literature sources. It has been argued that unification of the method with cluster techniques would make possible the treatment of realistic lattice models with multi-spin interactions and describe in a unified framework the phase transitions of any kind. Besides the RG equations the layer-cake technique can be used in the exact partial renormalization of the local interactions in the functional lattice Hamiltonians. This procedure reduces the strength of the interactions which in some cases can make them amenable to perturbative treatment.A self-consistent renormalization scheme suitable for the calculation of non-universal quantities in $n$-vector models with pair spin interactions of arbitrary extent has been suggested. The method has been based on the elimination of the fluctuating field components within the layers defined by the layer-cake representation of the propagator. The non-perturbative renormalization group (RG) equations has been solved in the local potential approximation. Critical temperatures of the $n=1-3$ vector spin models on cubic lattices have been calculated in excellent agreement with the best known estimates. Several critical amplitudes and the magnetisation curve of the Ising model on the simple cubic lattice calculated within the approach compared well with the values from literature sources. It has been argued that unification of the method with cluster techniques would make possible the treatment of realistic lattice models with multi-spin interactions and describe in a unified framework the phase transitions of any kind. Besides the RG equations the layer-cake technique can be used in the exact partial renormalization of the local interactions in the functional lattice Hamiltonians. This procedure reduces the strength of the interactions which in some cases can make them amenable to perturbative treatment.

arXiv:1904.10338Apr 23, 20192 citations

Mean field renormalization group approach to lattice models

Attilio L. Stella

Springer eBooksNov 13, 20051 citation

Renormalization Group on the Lattice

Andreas Wipf

Lecture notes in physicsOct 26, 20120 citations

A non-perturbative approach to critical dynamics

Léonie Canet, Hugues Chaté

This paper is devoted to a non-perturbative renormalization group (NPRG) analysis of Model A, which stands as a paradigm for the study of critical dynamics. The NPRG formalism has appeared as a valuable theoretical tool to investigate non-equilibrium critical phenomena, yet the simplest—and nontrivial—models for critical dynamics have never been studied using NPRG techniques. In this paper we focus on Model A taking this opportunity to provide a pedagogical introduction to NPRG methods for dynamical problems in statistical physics. The dynamical exponent z is computed in d = 3 and d = 2 and is found to be in close agreement with results from other methods.This paper is devoted to a non-perturbative renormalization group (NPRG) analysis of Model A, which stands as a paradigm for the study of critical dynamics. The NPRG formalism has appeared as a valuable theoretical tool to investigate non-equilibrium critical phenomena, yet the simplest—and nontrivial—models for critical dynamics have never been studied using NPRG techniques. In this paper we focus on Model A taking this opportunity to provide a pedagogical introduction to NPRG methods for dynamical problems in statistical physics. The dynamical exponent z is computed in d = 3 and d = 2 and is found to be in close agreement with results from other methods.

arXiv:cond-mat/0610468Journal of Physics A Mathematical and TheoreticalFeb 14, 200764 citations

Nonperturbative Renormalization Group

Taiki Haga

Springer thesesJan 1, 20190 citations

Lattice study of RG flow in 2D $\phi^4$ theoryLattice study of RG flow in 2D $\phi^4$ theory

Shashank Sharma, Dipankar Chakrabarti, Vipul Arora

Gradient flow method provides a practical framework for implementing Renormalization Group (RG) transformations on the lattice, commonly referred to as the Gradient Flow Renormalization Group (GFRG). In this work, we investigate the RG flow of the two-dimensional scalar $\phi^4$ theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.Gradient flow method provides a practical framework for implementing Renormalization Group (RG) transformations on the lattice, commonly referred to as the Gradient Flow Renormalization Group (GFRG). In this work, we investigate the RG flow of the two-dimensional scalar $\phi^4$ theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.

International Symposium on Lattice Field Theory (LATTICE)Jun 29, 20260 citations

A self-consistent renormalization scheme suitable for the calculation of non-universal quantities in

n

-vector models with pair spin interactions of arbitrary extent has been suggested. The method has been based on the elimination of the fluctuating field components within the layers defined by the layer-cake representation of the propagator. The non-perturbative renormalization group (RG) equations has been solved in the local potential approximation. Critical temperatures of the

n=1-3

vector spin models on cubic lattices have been calculated in excellent agreement with the best known estimates. Several critical amplitudes and the magnetisation curve of the Ising model on the simple cubic lattice calculated within the approach compared well with the values from literature sources. It has been argued that unification of the method with cluster techniques would make possible the treatment of realistic lattice models with multi-spin interactions and describe in a unified framework the phase transitions of any kind. Besides the RG equations the layer-cake technique can be used in the exact partial renormalization of the local interactions in the functional lattice Hamiltonians. This procedure reduces the strength of the interactions which in some cases can make them amenable to perturbative treatment.

Lattice study of RG flow in 2D

\phi^4

theory

\phi^4

theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.