Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills

TL;DR

This paper explores the finite size scaling of Fisher Zeroes in relation to critical slowing down in Quantum Monte Carlo methods, and discusses applications to N=4 Super Yang-Mills theory and quantum corrections.

Contribution

It introduces a novel connection between Fisher Zeroes scaling and the dynamical gap, and applies this to analyze quantum corrections in N=4 SYM.

Findings

Finite size scaling relates Fisher Zeroes to the dynamical gap.

Scaling arguments provide insights into quantum corrections in N=4 SYM.

Potential extension to higher twist parton distributions.

Abstract

We investigate critical slowing down in the local updating continuous-time Quantum Monte Carlo method by relating the finite size scaling of Fisher Zeroes to the dynamically generated gap, through the scaling of their respective critical exponents. As we comment, the nonlinear sigma model representation derived through the hamiltonian of our lattice spin model can also be used to give a effective treatment of planar anomalous dimensions in N=4 SYM. We present scaling arguments from our FSS analysis to discuss quantum corrections and recent 2-loop results, and further comment on the prospects of extending this approach for calculating higher twist parton distributions.