Functional integral approach to multipoint correlators in 2d critical systems

TL;DR

This paper extends a functional integral technique to compute multipoint correlators in 2D critical systems, providing new proofs and insights into critical exponents and correlator formulas.

Contribution

It introduces a novel extension of a functional integral method for multipoint correlators and offers a rigorous proof of exponent relations in 2D critical models.

Findings

Derivation of Kadanoff-Ceva's formula using the new method

Evaluation of the polarization operator's critical exponent in the Baxter model

Rigorous proof of exponent relations in the path-integral framework

Abstract

We extend a previously developed technique for computing spin-spin critical correlators in the 2d Ising model, to the case of multiple correlations. This enables us to derive Kadanoff-Ceva's formula in a simple and elegant way. We also exploit a doubling procedure in order to evaluate the critical exponent of the polarization operator in the Baxter model. Thus we provide a rigorous proof of the relation between different exponents, in the path-integral framework.