3D Ising Model: a view from the Conformal Bootstrap Island

TL;DR

This paper discusses how conformal bootstrap methods, based on axioms of Conformal Field Theory, predict critical exponents for 3D phase transitions by constraining correlation functions within a small parameter space island.

Contribution

It demonstrates how conformal bootstrap techniques can precisely determine critical exponents in three-dimensional systems, refining previous estimates.

Findings

Critical exponents lie within a small parameter space island.

Conformal invariance imposes strong constraints on correlation functions.

Numerical analysis confirms the consistency of the conformal bootstrap predictions.

Abstract

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space.