Extended scaling relations for planar lattice models

TL;DR

This paper proves some extended scaling relations for planar lattice models like the Eight Vertex and Ashkin-Teller models, confirming conjectures derived from their effective quantum field theories.

Contribution

It provides rigorous proof for certain extended scaling relations among critical indices, validating previous conjectures by Kadanoff and Luther-Peschel.

Findings

Proved validity of some extended scaling relations

Confirmed conjectures by Kadanoff and Luther-Peschel

Supports the effective quantum field theory approach

Abstract

It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theory obtained as formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones by Kadanoff, [K], and by Luther and Peschel, [LP].