Calculation of non-universal thermodynamic quantities within self-consistent non-perturbative functional renormalization group approach

TL;DR

This paper introduces a self-consistent non-perturbative functional renormalization group method for calculating non-universal thermodynamic quantities in vector spin models, achieving accurate critical temperature estimates and promising broader applications.

Contribution

The authors develop a novel RG approach based on the layer-cake representation, enabling precise calculation of non-universal quantities in lattice models with arbitrary spin interactions.

Findings

Critical temperatures match well with known estimates.

Calculated critical amplitudes and magnetization curves agree with literature.

Method shows potential for unifying with cluster techniques for complex models.

Abstract

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.