Finite size scaling and triviality of \phi^4 theory on an antiperiodic torus

TL;DR

This paper investigates the triviality of four-dimensional 3^4 theory using worm algorithms with antiperiodic boundary conditions, finding improved agreement with perturbation theory and insights into finite size scaling.

Contribution

It extends worm methods to antiperiodic boundary conditions and formulates finite size renormalization schemes to study 3^4 theory's triviality.

Findings

Antiperiodic boundary conditions eliminate zero momentum modes.

Closer agreement with perturbation theory is achieved.

Finite size effects are systematically analyzed.

Abstract

Worm methods to simulate the Ising model in the Aizenman random current representation including a low noise estimator for the connected four point function are extended to allow for antiperiodic boundary conditions. In this setup several finite size renormalization schemes are formulated and studied with regard to the triviality of \phi^4 theory in four dimensions. With antiperiodicity eliminating the zero momentum Fourier mode a closer agreement with perturbation theory is found compared to the periodic torus.