Universal Relations for Non Solvable Statistical Models

TL;DR

This paper rigorously derives universal relations for complex statistical models with varying parameters, extending known conjectures and introducing new formulas for models lacking exact solutions.

Contribution

It provides the first rigorous derivation of universal relations for non-solvable models like interacting Ising and quantum spin chains, confirming and extending previous conjectures.

Findings

Validated several conjectured universal relations.

Derived a novel relation for the anisotropic Ashkin-Teller model.

Extended the understanding of universal behaviors in complex models.

Abstract

We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, Haldane, but only checked in the special solvable models; one of them, related to the anisotropic Ashkin-Teller model, is novel.