Exact Strongly Coupled Fixed Point in $g\varphi^4$ Theory

TL;DR

This paper constructs an explicit strongly coupled fixed point in scalar gϕ^4 theory for dimensions less than 4, revealing unique critical exponents and implications for 2D Mott systems.

Contribution

It introduces a novel method to explicitly construct a strongly coupled fixed point in gϕ^4 theory using a non-linear eigenvalue problem, with specific critical exponents and physical predictions.

Findings

Fixed point exists only for d<4

Exponents match 2D Ising model at d=2

Predicts vanishing specific heat exponent

Abstract

We show explicitly how a strongly coupled fixed point can be constructed in scalar $g\varphi^4$ theory from the solutions to a non-linear eigenvalue problem. The fixed point exists only for $d< 4$, is unstable and characterized by $\nu=2/d$ (correlation length exponent), $\eta=1/2-d/8$ (anomalous dimension). For $d=2$, these exponents reproduce to those of the Ising model which can be understood from the codimension of the critical point. At this fixed point, $\varphi^{2i}$ terms with $i>2$ are all irrelevant. The testable prediction of this fixed point is that the specific heat exponent vanishes. 2d critical Mott systems are well described by this new fixed point.